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Detecting a Higgs Pseudoscalar with a Z Boson at the LHC ; We have adopted two Higgs doublet models to study the production of a Higgs pseudoscalar A0 in association with a Z gauge boson from gluon fusion gg to ZA0 at the CERN Large Hadron Collider. The prospects for the discovery of ZA0 to ell barell bbarb are investigated with physics backgrounds and realistic cuts. Promising results are found for mA alt 260 GeV in two Higgs doublet models when the heavier Higgs scalar H0 can decay into a Z boson and a Higgs pseudoscalar A0. Although the cross section of gg to ZA0 is usually small in the minimal supersymmetric standard model, it can be significantly enhanced in general two Higgs doublet models. This discovery channel might provide an opportunity to search for a Higgs scalar and a Higgs pseudoscalar simultaneously at the LHC and could lead to new physics beyond the Standard Model and the minimal supersymmetric model.

Dilaton and Moduli Fields in Dterm inflation ; We investigate the possibility of Dterm inflation within the framework of type I stringinspired models. Although Dterm inflation model has the excellent property that it is free from the socalled eta problem, two serious problems appear when we embed Dterm inflation in string theory, the magnitude of FI term and the rolling motion of the dilation. In the present paper, we analyze the potential of Dterm inflation in type I inspired models and study the behavior of dilaton and twisted moduli fields. Adopting the nonperturbative superpotential induced by gaugino condensation, the twisted moduli can be stabilized. If the dilaton is in a certain range, it evolves very slowly and does not run away to infinity. Thus Dterm dominated vacuum energy becomes available for driving inflation. By studying the density perturbation generated by the inflation model, we derive the constraints on model parameters and give some implications on Dterm inflation in type I inspired models.

Macroscopic description of preheating ; We present a macroscopic model of the decay of a coherent classical scalar field into statistical fluctuations through the process of parametric amplification. We solve the field theory henceforth,microscopic model to leading order in a Large N expansion, and show that the macroscopic model gives satisfactory results for the evolution of the field, its conjuguate momentum and the energy momentum tensor of the fluctuations over many oscillations. The macroscopic model is substantially simpler then the microscopic one, and can be easily generalized to include quantum fluctuations. Although we assume here and homogeneous situation, the model is fully covariant, and can be applied in inhomogeneous cases as well. These features make this a promising model in exploring the physics of preheating.

Minimal Flavour Violation ; These lectures give a description of models with minimal flavour violation MFV that can be tested in B and K meson decays. This class of models can be formulated to a very good approximation in terms of 11 parameters 4 parameters of the CKM matrix and 7 values of the it universal master functions Fr that parametrize the short distance contributions. In a given MFV model, Fr can be calculated in perturbation theory and are generally correlated with each other but in a model independent analysis they must be considered as free parameters. We conjecture that only 5 or even only 4 of these functions receive significant new physics contributions. We summarize the status of the CKM matrix, outline strategies for the determination of the values of Fr and present a number of relations between physical observables that do not depend on Fr at all. We emphasize that the formulation of MFV in terms of master functions allows to study transparently correlations between B and K decays which is very difficult if Wilson coefficients normalized at low energy scales are used instead. We discuss briefly a specific MFV model the Standard Model with one universal large extra dimension.

Neutrino Mass Models in Extra Dimensions ; Neutrinos play a crucial role in many areas of physics from very short distances to astrophysics and cosmology. It is a long held believe that they are good probes of physics at the GUT scale. Recent developments have made it clear that they can also be of fundamental importance for the physics of extra dimensions if these exist. Here we pedagogically review the construction of neutrino mass models in extra dimensions within the brane world scenarios. These models are usually nontrivial generalizations of their four dimensional counterparts. We describe the theoretical tools that have been forged and the new perpectives gained in this rapidly developing area. In particular we discuss the issues involve in building models without the use of righthanded singlets. It is very difficult to directly test the origin of neutrino masses in different models be it in four or more dimensions. We point out that different models give very different indirect signatures in the TeV region and in precision measurements.

The New Minimal Standard Model ; We construct the New Minimal Standard Model that incorporates the new discoveries of physics beyond the Minimal Standard Model MSM Dark Energy, nonbaryonic Dark Matter, neutrino masses, as well as baryon asymmetry and cosmic inflation, adopting the principle of minimal particle content and the most general renormalizable Lagrangian. We base the model purely on empirical facts rather than aesthetics. We need only six new degrees of freedom beyond the MSM. It is free from excessive flavorchanging effects, CP violation, toorapid proton decay, problems with electroweak precision data, and unwanted cosmological relics. Any model of physics beyond the MSM should be measured against the phenomenological success of this model.

Localized Supersoft Supersymmetry Breaking ; We consider supersymmetry breaking models in which the MSSM is extended to include an additional chiral adjoint field for each gauge group with which the the MSSM gauginos acquire Dirac masses. We investigate a framework in which the Standard Model gauge fields propagate in the bulk of a warped extra dimension while quarks and leptons are localized on the ultraviolet brane. The adjoint fields are localized on the infrared brane, where supersymmetry is broken in a hidden sector. This setup naturally suppresses potentially large flavor violating effects, while allowing perturbative gauge coupling unification under SU5 to be realized. The Standard Model superpartner masses exhibit a supersoft spectrum. Since the soft scalar masses are generated at very low scales of order the gaugino masses these models are significantly less finetuned than other supersymmetric models. The LSP in this class of models is the gravitino, while the NLSP is the stau. We show that this theory has an approximate R symmetry under which the gauginos are charged. This symmetry allows several possibilities for experimentally distinguishing the Dirac nature of the gauginos.

Testing an Optimised Expansion on Z2 Lattice Models ; We test an optimised hopping parameter expansion on various Z2 lattice scalar field models the Ising model, a spinone model and lambda phi4. We do this by studying the critical indices for a variety of optimisation criteria, in a range of dimensions and with various trial actions. We work up to seventh order, thus going well beyond previous studies. We demonstrate how to use numerical methods to generate the high order diagrams and their corresponding expressions. These are then used to calculate results numerically and, in the case of the Ising model, we obtain some analytic results. We highlight problems with several optimisation schemes and show for the best scheme that the critical exponents are consistent with mean field results to at least 8 significant figures. We conclude that in its present form, such optimised lattice expansions do not seem to be capturing the nonperturbative infrared physics near the critical points of scalar models.

Decoupling SupersymmetryHiggs without finetuning ; We propose a simple superpotential for the Higgs doublets, where the electroweak symmetry is broken at the supersymmetric level. We show that, for a class of supersymmetry breaking scenarios, the electroweak scale can be stable even though the supersymmetry breaking scale is much higher than it. Therefore, all the superpartners and the Higgs bosons can be decoupled from the electroweak scale, nevertheless no finetuning is needed. We present a concrete model, as an existence proof of such a model, which generates the superpotential dynamically. According to supersymmetry breaking scenarios to be concerned, various phenomenological applications of our model are possible. For example, based on our model, the recently proposed split supersymmetry'' scenario can be realized without finetuning. If the electroweak scale supersymmetry breaking is taken into account, our model provides a similar structure to the recently proposed fat Higgs'' model and the upper bound on the lightest Higgs boson mass can be relaxed.

Strong CP, Flavor, and Twisted Split Fermions ; We present a natural solution to the strong CP problem in the context of split fermions. By assuming CP is spontaneously broken in the bulk, a weak CKM phase is created in the standard model due to a twisting in flavor space of the bulk fermion wavefunctions. But the strong CP phase remains zero, being essentially protected by parity in the bulk and CP on the branes. As always in models of spontaneous CP breaking, radiative corrections to theta bar from the standard model are tiny, but even higher dimension operators are not that dangerous. The twisting phenomenon was recently shown to be generic, and not to interfere with the way that split fermions naturally weaves small numbers into the standard model. It follows that out approach to strong CP is compatible with flavor, and we sketch a comprehensive model. We also look at deconstructed version of this setup which provides a viable 4D model of spontaneous CP breaking which is not in the NelsonBarr class.

Lepton Flavor Violation in Extra Dimension Models ; Models involving large extra spatial dimensions have interesting predictions on lepton flavor violating processes. We consider some 5D models which are related to neutrino mass generation or address the fermion masses hierarchy problem. We study the signatures in low energy experiments that can discriminate the different models. The focus is on muonelectron conversion in nuclei, mura e gamma and mura 3e processes and their tau counterparts. Their links with the active neutrino mass matrix are investigated. We show that in the models we discussed the branching ratio of mura e gamma like rare process is much smaller than the ones of mura 3e like processes. This is in sharp contrast to most of the traditional wisdom based on four dimensional gauge models. Moreover, some rare tau decays are more promising than the rare muon decays.

A Minimally FineTuned Supersymmetric Standard Model ; We construct supersymmetric theories in which the correct scale for electroweak symmetry breaking is obtained without significant finetuning. We calculate the finetuning parameter for these theories to be at the 20 level, which is significantly better than in conventional supersymmetry breaking scenarios. Supersymmetry breaking occurs at a low scale of order 100 TeV, and is transmitted to the supersymmetric standardmodel sector through standardmodel gauge interactions. The Higgs sector contains two Higgs doublets and a singlet field, with a superpotential that takes the most general form allowed by gauge invariance. An explicit model is constructed in 5D warped space with supersymmetry broken on the infrared brane. We perform a detailed analysis of electroweak symmetry breaking for this model, and demonstrate that the finetuning is in fact reduced. A new candidate for dark matter is also proposed, which arises from the extended Higgs sector of the model. Finally, we discuss a purely 4D theory which may also significantly reduce finetuning.

The FineTuning Problem in Little Higgs Models ; Little Higgs models represent an alternative to Supersymmetry as a solution to the Hierarchy Problem. After introducing the main physical ideas of these models, we present the finetuning associated to the electroweak breaking in Little Higgs scenarios. Taking into account the most general properties of this scenarios and focusing on two representative Little Higgs'' models, we find that the finetuning is much higher than suggested by the rough estimates usually made. The main sources that increase the finetuning in these models are identified, then they can be taken into account in order to construct a successful model.

Mixed heavyquarkgluon condensate in the stochastic vacuum model and dual superconductor ; The worldline formalism is used for the evaluation of the mixed heavyquarkgluon condensate in two models of QCD the stochastic vacuum model and the dual superconductor one. Calculations are performed for an arbitrary dimensionality of spacetime dge 2. While in the stochastic vacuum model, the condensate is UV finite up to d8, in the dual superconductor model it is UV divergent at any dge 2. A regularization of this divergence is proposed, which makes quantitative the condition of the typeII dual superconductor. The obtained results are generalized to the case of finite temperatures. Corrections to the both, mixed and standard, heavyquark condensates, which appear due to the variation of the gauge field at the scale of the vacuum correlation length, are evaluated within the stochastic vacuum model. These corrections diminish the absolute values of the condensates, as well as the ratio of the mixed condensate to the standard one.

Bounds on Low Scale Gravity from RICE data and Cosmogenic Neutrino Flux Models ; We explore limits on low scale gravity models set by results from the Radio Ice Cherenkov Experiment's RICE ongoing search for cosmic ray neutrinos in the cosmogenic, or GZK, energy range. The bound on MD, the fundamental scale of gravity, depends upon cosmogenic flux model, black hole formation and decay treatments, inclusion of graviton mediated elastic neutrino processes, and the number of large extra dimensions, d. Assuming protonbased cosmogenic flux models that cover a broad range of flux possibilities, we find bounds in the interval 0.9 TeV MD 10 TeV. Heavy nucleusbased models generally lead to smaller fluxes and correspondingly weaker bounds. Values d 5, 6 and 7, for which laboratory and astrophysical bounds on LSG models are less restrictive, lead to essentially the same limits on MD.

Effects of the littlest Higgs model with Tparity on Higgs boson production at high energy ee colliders ; The Higgs boson production processes eeto ZH, eeto barnuenueH, and eeto tbartH are very important for studying Higgs boson properties and further testing new physics beyond the standard modelSM in the high energy linear ee colliderILC. We estimate the contributions of the littlest Higgs model with TparityLHT model to these processes and find that the LHT model can generate significantly corrections to the production cross sections of these processes. We expect the possible signals of the LHT model can be detected via these processes in the future ILC experiments.

Effects of little Higgs models on single top production at the e colliders ; In the framework of the littlest HiggsLH model and the littlest Higgs model with TparityLHT, We investigate the single top production process egammato nuebbart, and calculate the corrections of these two models to the cross section of this process. We find that in the reasonable parameter space, the correction terms for the treelevel Wtb couplings coming from the LHT model can generate significantly corrections to the cross section of this process, which might be detected in the future high energy linear ee colliderILC experiments. However, the contributions of the new gauge boson WpmH predicted by the LH model to this process is very small.

AdSQCD Phenomenological Models from a BackReacted Geometry ; We construct a fully backreacted holographic dual of a fourdimensional field theory which exhibits chiral symmetry breaking. Two possible models are considered by studying the effects of a fivedimensional field, dual to the qbarq operator. One model has smooth geometry at all radii and the other dynamically generates a cutoff at finite radius. Both of these models satisfy Einstein's field equations. The second model has only three free parameters, as in QCD, and we show that this gives phenomenologically consistent results. We also discuss the possibility that in order to obtain linear confinement from a backreacted model it may be necessary to consider the condensate of a dimension two operator.

Metastable SUSY breaking within the Standard Model ; We construct a supersymmetric version of the Standard Model which contains a longlived metastable vacuum. In this vacuum supersymmetry is broken and the electroweak symmetry is Higgsed, and we identify it with the physical ground state of the Standard Model. In our approach the metastable supersymmetry breaking MSB occurs directly in the SU2L x U1Y sector of the Standard Model; it does not require a separate MSB sector and in this way it departs from the usual lore. There is a direct link between the electroweak symmetry breaking and the supersymmetry breaking in our model, both effects are induced by the same Higgs fields. In order to generate sufficiently large gluino masses we have to have strong coupling in the Higgs sector, h 1. Our model results in an extremely compact lowenergy effective theory at the electroweak scale with Higgs fields being very heavy, MHiggs MW and frozen at their vacuum expectation values.

The LiePoisson Structure of Integrable Classical NonLinear Sigma Models ; The canonical structure of classical nonlinear sigma models on Riemannian symmetric spaces, which constitute the most general class of classical nonlinear sigma models known to be integrable, is shown to be governed by a fundamental Poisson bracket relation that fits into the rsmatrix formalism for nonultralocal integrable models first discussed by Maillet. The matrices r and s are computed explicitly and, being field dependent, satisfy fundamental Poisson bracket relations of their own, which can be expressed in terms of a new numerical matrixc. It is proposed that all these Poisson brackets taken together are representation conditions for a new kind of algebra which, for this class of models, replaces the classical YangBaxter algebra governing the canonical structure of ultralocal models. The Poisson brackets for the transition matrices are also computed, and the notorious regularization problem associated with the definition of the Poisson brackets for the monodromy matrices is discussed.

The On model on a random surface critical points and large order behaviour ; In this article we report a preliminary investigation of the large N limit of a generalized onematrix model which represents an On symmetric model on a random lattice. The model on a regular lattice is known to be critical only for 2le nle 2. This is the situation we shall discuss also here, using steepest descent. We first determine the critical and multicritical points, recovering in particular results previously obtained by Kostov. We then calculate the scaling behaviour in the critical region when the cosmological constant is close to its critical value. Like for the multimatrix models, all critical points can be classified in terms of two relatively prime integers p,q. In the parametrization p2m1q pm l, m,l integers such that 0lq, the string susceptibility exponent is found to be gammarm string2lpql. When l1 we find that all results agree with those of the corresponding p,q string models, otherwise they are different.par We finally explain how to derive the large order behaviour of the corresponding topological expansion in the double scaling limit.

A Study of Two Dimensional String Theory PhD Thesis ; This thesis is a study of two dimensional noncritical string theory. The main tool which is used, is the matrix model. Introductions to both the Liouville model and its matrix model formulation are included. In particular the special states are discussed. Some calculations of partition functions on genus one using field theory techniques are given. Nonperturbative issues and string theory at finite radius are discussed. Zero momentum correlation functions are calculated using the matrix model. One important result is a set of recursion relations. The treatment is extended to nonzero momentum. The main result is a clear identification of the special states. Some comments on the Wheeler de Witt equation is given. The matrix model Winfty algebra is introduced. This organizes the previous results. In particular, a simple derivation of the genus zero tachyon correlation functions is given. The results are then extended to higher genus. It is seen how a deformation of the algebra is responsible for much of the higher genus structure. Some very explicit formulae are derived. Then the Liouville and matrix model calculations are compared followed by some general conclusions.

Conformal Matrix Models as an Alternative to Conventional MultiMatrix Models ; We introduce it conformal multimatrix models CMM as an alternative to conventional multimatrix model description of twodimensional gravity interacting with c 1 matter. We define CMM as solutions to discrete extended Virasoro constraints. We argue that the so defined alternatives of multimatrix models represent the same universality classes in continuum limit, while at the discrete level they provide explicit solutions to the multicomponent KP hierarchy and by definition satisfy the discrete Wconstraints. We prove that discrete CMM coincide with the p,qseries of 2d gravity models in a it wellit defined continuum limit, thus demonstrating that they provide a proper generalization of Hermitian onematrix model.

Superconformal theories from Pseudoparticle Mechanics ; We consider a onedimensional OspN2M pseudoparticle mechanical model which may be written as a phase space gauge theory. We show how the pseudoparticle model naturally encodes and explains the twodimensional zero curvature approach to finding extended conformal symmetries. We describe a procedure of partial gauge fixing of these theories which leads generally to theories with superconformally extended cal Walgebras. The pseudoparticle model allows one to derive the finite transformations of the gauge and matter fields occurring in these theories with extended conformal symmetries. In particular, the partial gauge fixing of the OspN2 pseudoparticle mechanical models results in theories with the SON invariant Nextended superconformal symmetry algebra of Bershadsky and Knizhnik. These algebras are nonlinear for N geq 3. We discuss in detail the cases of N1 and N2, giving two new derivations of the superschwarzian derivatives. Some comments are made in the N2 case on how twisted and topological theories represent a significant deformation of the original particle model. The particle model also allows one to interpret superconformal transformations as deformations of flags in super jet bundles over the associated super Riemann surface.

New Realisations of Minimal Models and the Structure of WStrings ; The quantization of a free boson whose momentum satisfies a cubic constraint leads to a cha conformal field theory with a BRST symmetry. The theory also has a Winfty symmetry in which all the generators except the stresstensor are BRSTexact and so topological. The BRST cohomology includes states of conformal dimensions 0,si,ha, together with lq copies' of these states obtained by acting with picturechanging and screening operators. The 3point and 4point correlation functions agree with those of the Ising model, suggesting that the theory is equivalent to the critical Ising model. At tree level, the W3 string can be viewed as an ordinary c26 string whose conformal matter sector includes this realisation of the Ising model. The twoboson W3 string is equivalent to the Ising model coupled to twodimensional quantum gravity. Similar results apply for other Wstrings and minimal models.

Integrable Perturbations of Wn and WZW Models ; We present a new class of 2d integrable models obtained as perturbations of minimal CFT with Wsymmetry by fundamental weight primaries. These models are generalisations of well known 1,2perturbed Virasoro minimal models. In the large p number of minimal model limit they coincide with scalar perturbations of WZW theories. The algebra of conserved charges is discussed in this limit. We prove that it is noncommutative and coincides with twisted affine algebra G represented in a space of asymptotic states. We conjecture that scattering in these models for generic p is described by Smatrix of the qdeformed G algebra with q being root of unity.

Fusion Hierarchy and FiniteSize Corrections of Uqsl2 Invariant Vertex Models with Open Boundaries ; The fused sixvertex models with open boundary conditions are studied. The Bethe ansatz solution given by Sklyanin has been generalized to the transfer matrices of the fused models. We have shown that the eigenvalues of transfer matrices satisfy a group of functional relations, which are the su2 fusion rule held by the transfer matrices of the fused models. The fused transfer matrices form a commuting family and also commute with the quantum group Uqsl2. In the case of the parameter qh1 h4,5,cdots the functional relations in the limit of spectral parameter uto iinfty are truncated. This shows that the su2 fusion rule with finite level appears for the six vertex model with the open boundary conditions. We have solved the functional relations to obtain the finitesize corrections of the fused transfer matrices for lowlying excitations. From the corrections the central charges and conformal weights of underlying conformal field theory are extracted. To see different boundary conditions we also have studied the sixvertex model with a twisted boundary condition.

Topological Models and LargeN Matrix Integral ; In this paper we describe in some detail the representation of the topological CP1 model in terms of a matrix integral which we have introduced in a previous article. We first discuss the integrable structure of the CP1 model and show that it is governed by an extension of the 1dimensional Toda hierarchy. We then introduce a matrix model which reproduces the sum over holomorphic maps from arbitrary Riemann surfaces onto CP1. We compute intersection numbers on the moduli space of curves using geometrical method and show that the results agree with those predicted by the matrix model. We also develop a LandauGinzburg LG description of the CP1 model using a superpotential eXet0,QeX given by the Lax operator of the Toda hierarchy X is the LG field and t0,Q is the coupling constant of the Kahler class. The form of the superpotential indicates the close connection between CP1 and N2 supersymmetric sineGordon theory which was noted some time ago by several authors. We also discuss possible generalizations of our construction to other manifolds and present a LG formulation of the topological CP2 model.

BATALINFRADKINTYUTIN EMBEDDING OF A SELFDUAL MODEL AND THE MAXWELLCHERNSIMONS THEORY ; We convert the selfdual model of Townsend, Pilch, and Nieuwenhuizen to a firstclass system using the generalized canonical formalism of Batalin, Fradkin, and Tyutin and show that gaugeinvariant fields in the embedded model can be identified with observables in the MaxwellChernSimons theory as well as with the fundamental fields of the selfdual model. We construct the phasespace partition function of the embedded model and demonstrate how a basic set of gaugevariant fields can play the role of either the vector potentials in the MaxwellChernSimons theory or the fundamental fields of the selfdual model by appropriate choices of gauge.

Exact Results And Soft Breaking Masses In Supersymmetric Gauge Theory ; We give an explicit formalism connecting softly broken supersymmetric gauge theories with QCD as one limit to N2 and N1 supersymmetric theories possessing exact solutions, using spurion fields to embed these models in an enlarged N1 model. The functional forms of effective Lagrangian terms resulting from soft supersymmetry breaking are constrained by the symmetries of the enlarged model, although not well enough to fully determine the vacuum structure of generic softly broken models. Nevertheless by perturbing the exact N1 model results with sufficiently small soft breaking masses, we show that there exist nonsupersymmetric models that exhibit monopole condensation and confinement in the same modes as the N1 case.

Solution of the SL2,R string in curved spacetime ; The SL2,R WZW model, one of the simplest models for strings propagating in curved space time, was believed to be nonunitary in the algebraic treatment involving affine current algebra. It is shown that this was an error that resulted from neglecting a zero mode that must be included to describe the correct physics of noncompact WZW models. In the presence of the zero mode the massshell condition is altered and unitarity is restored. The correct currents, including the zero mode, have logarithmic cuts on the worldsheet. This has physical consequences for the spectrum because a combination of zero modes must be quantized in order to impose periodic boundary conditions on mass shell in the physical sector. To arrive at these results and to solve the model completely, the SL2,R WZW model is quantized in a free field formalism that differs from previous ones in that the fields and the currents are Hermitean, there are cuts, and there is a new term that could be present more generally, but is excluded in the WZW model.

Integrable FourFermi Models with a Boundary and BosonFermion Duality ; Construction of integrable field theories in space with a boundary is extended to fermionic models. We obtain general forms of boundary interactions consistent with integrability of the massive Thirring model and study the duality equivalence of the MT model and the sineGordon model with boundary terms. We find a variety of integrable boundary interactions in the O3 GrossNeveu model from the boundary supersymmetric sineGordon theory by using bosonfermion duality.

On Duality of Twodimensional Ising Model on Finite Lattice ; It is shown that the partition function of the 2d Ising model on the dual finite lattice with periodical boundary conditions is expressed through some specific combination of the partition functions of the model on the torus with corresponding boundary conditions. The generalization of the duality relations for the nonhomogeneous case is given. These relations are proved for the weaklynonhomogeneous distribution of the coupling constants for the finite lattice of arbitrary sizes. Using the duality relations for the nonhomogeneous Ising model, we obtain the duality relations for the twopoint correlation function on the torus, the 2d Ising model with magnetic fields applied to the boundaries and the 2d Ising model with free, fixed and mixed boundary conditions.

Models of Dynamical Supersymmetry Breaking from a SU2k3 Model ; We investigate three classes of supersymmetric models which can be obtained by breaking the chiral SU2k3 gauge theories with one antisymmetric tensor and 2k1 antifundamentals. For N3, the chiral SU2ktimesSU3timesU1 theories break supersym metry by the quantum deformations of the moduli spaces in the strong SU2k gauge coupling limit. For N2, it is the generalization of the SU5timesU2timesU1 model mentioned in the literature. Supersymmetry is broken by carefully choosing the q uarkantiquarkdoublet Yukawa couplings in this model. For N1, this becomes the wellknown model discussed in the literature.

Symmetry, Integrable Chain Models and Stochastic Processes ; A general way to construct chain models with certain Lie algebraic or quantum Lie algebraic symmetries is presented. These symmetric models give rise to series of integrable systems. As an example the chain models with An symmetry and the related TemperleyLieb algebraic structures and representations are discussed. It is shown that corresponding to these An symmetric integrable chain models there are exactly solvable stationary discretetime resp. continuoustime Markov chains whose spectra of the transition matrices resp. intensity matrices are the same as the ones of the corresponding integrable models.

Classical anomalies for spinning particles ; We discuss the phenomenon of classical anomaly. It is observed for 3D BerezinMarinov BM, BarducciCasalbuoniLusanna BCL and CortesPlyushchayVelazquez CPV pseudoclassical spin particle models. We show that quantum mechanically these different models correspond to the same P,Tinvariant system of planar fermions, but the quantum system has global symmetries being not reproducible classically in full in any of the models. We demonstrate that the specific U1 gauge symmetry characterized by the opposite coupling constants of spin s12 and s12 states has a natural classical analog in CPV model but can be reproduced in BM and BCL models in an obscure and rather artificial form. We also show that BM and BCL models quantum mechanically are equivalent in any odddimensional spacetime, but describe different quantum systems in even spacetime dimensions.

Boundary flows in minimal models ; We discuss in this paper the behaviour of minimal models of conformal theory perturbed by the operator Phi13 at the boundary. Using the RSOS restriction of the sineGordon model, adapted to the boundary problem, a series of boundary flows between different set of conformally invariant boundary conditions are described. Generalizing the staircase phenomenon discovered by Al. Zamolodchikov, we find that an analytic continuation of the boundary sinhGordon model provides a flow interpolation not only between all minimal models in the bulk, but also between their possible conformal boundary conditions. In the particular case where the bulk sinhGordon coupling is turned to zero, we obtain a boundary roaming trajectory in the c1 theory that interpolates between all the possible spin S Kondo models.

Boundary Flows in general Coset Theories ; In this paper we study the boundary effects for offcritical integrable field theories which have close analogs with integrable lattice models. Our models are the SU2kotimes SU2lSU2kl coset conformal field theories perturbed by integrable boundary and bulk operators. The boundary interactions are encoded into the boundary reflection matrix. Using the TBA method, we verify the flows of the conformal BCs by computing the boundary entropies. These flows of the BCs have direct interpretations for the fusion RSOS lattice models. For super CFTs k2 we show that these flows are possible only for the NeveuSchwarz sector and are consistent with the lattice results. The models we considered cover a wide class of integrable models. In particular, we show how the the impurity spin is screened by electrons for the kchannel Kondo model by taking ltoinfty limit. We also study the problem using an independent method based on the boundary roaming TBA. Our numerical results are consistent with the boundary CFTs and RSOS TBA analysis.

U1xSUm1 Theory and cm W1infty Minimal Models in the Hierarchical Quantum Hall Effect ; Two classes of Conformal Field Theories have been proposed to describe the Hierarchical Quantum Hall Effectthe multicomponent bosonic theory, characterized by the symmetry U1xSUm1 and the W1infty minimal models with central charge cm. In spite of having the same spectrum of edge excitations, they manifest differences in the degeneracy of the states and in the quantum statistics, which call for a more detailed comparison between them. Here, we describe their detailed relation for the general case, cm and extend the methods previously published for c 4. Specifically, we obtain the reduction in the number of degrees of freedom from the multicomponent Abelian theory to the minimal models by decomposing the characters of the U1xSUm1 representations into those of the cm W1infty minimal models. Furthermore, we find the Hamiltonian whose renormalization group flow interpolates between the two models, having the W1infty minimal models as infrared fixed point.

Generalized 2D BF Model quantized in the axial gauge ; We discuss the ultraviolet finiteness of the twodimensional BF model coupled to topological matter quantized in the axial gauge. This noncovariant gauge fixing avoids the infrared problem in the twodimensional spacetime. The BF model together with the matter coupling is obtained by dimensional reduction of the ordinary threedimensional BF model. This procedure furnishes the usual linear vector supersymmetry and an additional scalar supersymmetry. The whole symmetry content of the model allows to apply the standard algebraic renormalization procedure which we use to prove that this model is ultraviolet finite and anomaly free to all orders of perturbation theory.

Three loop renormalization of the SUNc nonabelian Thirring model ; We renormalize to three loops a version of the Thirring model where the fermion fields not only lie in the fundamental representation of a nonabelian colour group SUNc but also depend on the number of flavours, Nf. The model is not multiplicatively renormalizable in dimensional regularization due to the generation of evanescent operators which emerge at each loop order. Their effect in the construction of the true wave function, mass and coupling constant renormalization constants is handled by considering the projection technique to a new order. Having constructed the MSbar renormalization group functions we consider other massless independent renormalization schemes to ensure that the renormalization is consistent with the equivalence of the nonabelian Thirring model with other models with a fourfermi interaction. One feature to emerge from the computation is the establishment of the fact that the SUNf Gross Neveu model is not multiplicatively renormalizable in dimensional regularization. An evanescent operator arises first at three loops and we determine its associated renormalization constant explicitly.

Correlators in integrable quantum field theory. The scaling RSOS models ; The study of the scaling limit of twodimensional models of statistical mechanics within the framework of integrable field theory is illustrated through the example of the RSOS models. Starting from the exact description of regime III in terms of colliding particles, we compute the correlation functions of the thermal, phi1,2 and for some cases spin operators in the twoparticle approximation. The accuracy obtained for the moments of these correlators is analysed by computing the central charge and the scaling dimensions and comparing with the exact results. We further consider the generally nonintegrable perturbation of the critical points with both the operators phi1,3 and phi1,2 and locate the branches solved on the lattice within the associated twodimensional phase diagram. Finally we discuss the fact that the RSOS models, the dilute qstate Potts model at and the On vector model are all described by the same perturbed conformal field theory.

A Small Cosmological Constant from a Large Extra Dimension ; We propose a new approach to the Cosmological Constant Problem which makes essential use of an extra dimension. A model is presented in which the Standard Model vacuum energy warps'' the higherdimensional spacetime while preserving 4D flatness. We argue that the strong curvature region of our solutions may effectively cut off the size of the extra dimension, thereby giving rise to macroscopic 4D gravity without a cosmological constant. In our model, the higherdimensional gravity dynamics is treated classically with carefully chosen couplings. Our treatment of the Standard Model is however fully quantum fieldtheoretic, and the 4D flatness of our solutions is robust against Standard Model quantum loops and changes to Standard Model couplings.

M theory as a matrix extension of ChernSimons theory ; We study a new class of matrix models, the simplest of which is based on an Sp2 symmetry and has a compactification which is equivalent to ChernSimons theory on the threetorus. By replacing Sp2 with the superalgebra Osp132, which has been conjectured to be the full symmetry group of M theory, we arrive at a supercovariant matrix model which appears to contain within it the previously proposed M theory matrix models. There is no background spacetime so that time and dynamics are introduced via compactifications which break the full covariance of the model. Three compactifications are studied corresponding to a hamiltonian quantization in D101, a Lorentz invariant quantization in D91 and a light cone gauge quantization in D11911. In all cases constraints arise which eliminate certain higher spin fields in terms of lower spin dynamical fields. In the SO9,1 invariant compactification we argue that the one loop effective action reduces to the IKKT covariant matrix model. In the light cone gauge compactification the theory contains the standard M theory light cone gauge matrix model, but there appears an additional transverse five form field.

Chiral Schwinger models without gauge anomalies ; We find a large class of quantum gauge models with massless fermions where the coupling to the gauge fields is not chirally symmetric and which nevertheless do not suffer from gauge anomalies. To be specific we study two dimensional Abelian models in the Hamiltonian framework which can be constructed and solved by standard techniques. The general model describes Np photon fields and Nf flavors of Dirac fermions with 2NfNp different coupling constants i.e. the chiral component of each fermion can be coupled to the gauge fields differently. We construct these models and find conditions so that no gauge anomaly appears. If these conditions hold it is possible to construct and solve the model explicitly, so that gauge and Lorentz invariance are manifest.

Chiral nonlinear sigmamodels as models for topological superconductivity ; We study the mechanism of topological superconductivity in a hierarchical chain of chiral nonlinear sigmamodels models of current algebra in one, two, and three spatial dimensions. The models have roots in the 1D PeierlsFrohlich model and illustrate how the 1D Frohlich's ideal conductivity extends to a genuine superconductivity in dimensions higher than one. The mechanism is based on the fact that a pointlike topological soliton carries an electric charge. We discuss a flux quantization mechanism and show that it is essentially a generalization of the persistent current phenomenon, known in quantum wires. We also discuss why the superconducting state is stable in the presence of a weak disorder.

Integrable Ladder tJ Model with Staggered Shift of the Spectral Parameter ; The generalization of the YangBaxter equations YBE in the presence of Z2 grading along both chain and time directions is presented and an integrable model of tJ type with staggered disposition along a chain of shifts of the spectral parameter is constructed. The Hamiltonian of the model is computed in fermionic formulation. It involves three neighbour site interactions and therefore can be considered as a zigzag ladder model. The Algebraic Bethe Ansatz technique is applied and the eigenstates, along with eigenvalues of the transfer matrix of the model are found. In the thermodynamic limit, the lowest energy of the model is formed by the quarter filling of the states by fermions instead of usual half filling.

Topologically Massive NonAbelian Gauge Theories Constraints and Deformations ; We study the relationship between three nonAbelian topologically massive gauge theories, viz. the naive nonAbelian generalization of the Abelian model, FreedmanTownsend model and the dynamical 2form theory, in the canonical framework. Hamiltonian formulation of the naive nonAbelian theory is presented first. The other two nonAbelian models are obtained by deforming the constraints of this model. We study the role of the auxiliary vector field in the dynamical 2form theory in the canonical framework and show that the dynamical 2form theory cannot be considered as the embedded version of naive nonAbelian model. The reducibility aspect and gauge algebra of the latter models are also discussed.

Remarks on topological models and fractional statistics ; One of the most intriguing aspects of ChernSimonstype topological models is the fractional statistics of point particles which has been shown essential for our understanding of the fractional quantum Hall effects. Furthermore these ideas are applied to the study of high Tc superconductivity. We present here an recently proposed model for fractional spin with the Pauli term. On the other hand, in D4 spacetime, a Schwarztype topological gauge theory with antisymmetric tensor gauge field, namely BF model, is reviewed. Antisymmetric tensor fields are conjectured as mediator of string interaction. A dimensional reduction of the previous model provides a 21 dimensional topological theory, which involves a 2form B and a 0form phi. Some recent results on this model are reported. Recently, there have been thoughts of generalizing unusual statistics to extended objects in others spacetime dimensions, and in particular to the case of strings in four dimensions. In this context, discussions about fractional spin and antisymmetric tensor field are presented.

Form factors from free fermionic Fock fields, the Federbush model ; By representing the field content as well as the particle creation operators in terms of fermionic Fock operators, we compute the corresponding matrix elements of the Federbush model. Only when these matrix elements satisfy the form factor consistency equations involving anyonic factors of local commutativity, the corresponding operators are local. We carry out the ultraviolet limit, analyze the momentum space cluster properties and demonstrate how the Federbush model can be obtained from the SU33homogeneous sineGordon model. We propose a new Lagrangian which on one hand constitutes a generalization of the Federbush model in a Lie algebraic fashion and on the other a certain limit of the homogeneous sineGordon models.

The Standard Model from Stable Intersecting Brane World Orbifolds ; We analyze the perturbative stability of nonsupersymmetric intersecting brane world models on tori. Besides the dilaton tadpole, a dynamical instability in the complex structure moduli space occurs at string disc level, which drives the background geometry to a degenerate limit. We show that in certain orbifold models this latter instability is absent as the relevant moduli are frozen. We construct explicit examples of such orbifold intersecting brane world models and discuss the phenomenological implications of a three generation Standard Model which descends naturally from an SU5 GUT theory. It turns out that various phenomenological issues require the string scale to be at least of the order of the GUT scale. As a major difference compared to the Standard Model, some of the Yukawa couplings are excluded so that the standard electroweak Higgs mechanism with a fundamental Higgs scalar is not realized in this setup.

E6 Matrix Model ; We consider a new matrix model based on the simply connected compact exceptional Lie group E6. A matrix ChernSimons theory is directly derived from the invariant on E6. It is stated that the similar argument as Smolin which derives an effective action of the matrix string type can also be held in our model. An important difference is that our model has twice as many degrees of freedom as Smolin's model has. One way to introduce the cosmological term is the compactification on directions. It is of great interest that the properties of the product space VecmathfrakJc times VecmathcalG, in which the degrees of freedom of our model live, are very similar to those of the physical Hilbert space.

On the symmetries of BF models and their relation with gravity ; The perturbative finiteness of various topological models e.g. BF models has its origin in an extra symmetry of the gaugefixed action, the socalled vector supersymmetry. Since an invariance of this type also exists for gravity and since gravity is closely related to certain BF models, vector supersymmetry should also be useful for tackling various aspects of quantum gravity. With this motivation and goal in mind, we first extend vector supersymmetry of BF models to generic manifolds by incorporating it into the BRST symmetry within the BatalinVilkovisky framework. Thereafter, we address the relationship between gravity and BF models, in particular for threedimensional spacetime.

Mutually local fields from form factors ; We compare two different methods of computing form factors. One is the well established procedure of solving the form factor consistency equations and the other is to represent the field content as well as the particle creation operators in terms of fermionic Fock operators. We compute the corresponding matrix elements for the complex free fermion and the Federbush model. The matrix elements only satisfy the form factor consistency equations involving anyonic factors of local commutativity when the corresponding operators are local. We carry out the ultraviolet limit, analyze the momentum space cluster properties and demonstrate how the Federbush model can be obtained from the SU33homogeneous sineGordon model. We propose a new class of Lagrangians which constitute a generalization of the Federbush model in a Lie algebraic fashion. For these models we evaluate the associated scattering matrices from first principles, which can alternatively also be obtained in a certain limit of the homogeneous sineGordon models.

Local models for intersecting brane worlds ; We describe the construction of configurations of D6branes wrapped on compact 3cycles intersecting at points in noncompact CalabiYau threefolds. Such constructions provide local models of intersecting brane worlds, and describe sectors of fourdimensional gauge theories with chiral fermions. We present several classes of noncompact manifolds with compact 3cycles intersecting at points, and discuss the rules required for model building with wrapped D6branes. The rules to build 3cycles are simple, and allow easy computation of chiral spectra, RR tadpoles and the amount of preserved supersymmetry. We present several explicit examples of these constructions, some of which have Standard Model like gauge group and three quarklepton generations. In some cases, mirror symmetry relates the models to other constructions used in phenomenological Dbrane model building, like Dbranes at singularities. Some simple N1 supersymmetric configurations may lead to relatively tractable G2 manifolds upon lift to Mtheory, which would be noncompact but nevertheless yield fourdimensional chiral gauge field theories.

Supergravity, Dark Energy and the Fate of the Universe ; We propose a description of dark energy and acceleration of the universe in extended supergravities with de Sitter dS solutions. Some of them are related to Mtheory with noncompact internal spaces. Masses of ultralight scalars in these models are quantized in units of the Hubble constant m2 n H2. If dS solution corresponds to a minimum of the effective potential, the universe eventually becomes dS space. If dS solution corresponds to a maximum or a saddle point, which is the case in all known models based on N8 supergravity, the flat universe eventually stops accelerating and collapses to a singularity. We show that in these models, as well as in the simplest models of dark energy based on N1 supergravity, the typical time remaining before the global collapse is comparable to the present age of the universe, t O1010 years. We discuss the possibility of distinguishing between various models and finding our destiny using cosmological observations.

Unifying Approaches in Integrable Systems Quantum and Statistical, Ultralocal and Nonultralocal ; The aim of this review is to present the list of by now a significant collection of quantum integrable models, ultralocal as well as nonultralocal, in a systematic way stressing on their underlying unifying algebraic structures. We restrict to quantum and statistical models belonging to trigonometric and rational classes with 2 x 2 Lax operators. The ultralocal models can be classified successfully through their associated quantum algebra and are governed by the YangBaxter equation, while the nonultralocal models, the theory of which is still in the developmental stage, allow systematization through the braided YangBaxter equation. Along with the known integrable models some possible directions for investigation in this field and generation of such new models are suggested.

Superconformal Selfdual SigmaModels ; A range of bosonic models can be expressed as sometimes generalized sigmamodels, with equations of motion coming from a selfduality constraint. We show that in D2, this is easily extended to supersymmetric cases, in a superspace approach. In particular, we find that the configurations of fields of a superconformal mathfrakGmathfrakH coset models which satisfy some selfduality constraint are automatically solutions to the equations of motion of the model. Finally, we show that symmetric space sigmamodels can be seen as infinitedimensional tfGtfH models constrained by a selfduality equation, with tfG the loop extension of mathfrakG and tfH a maximal subgroup. It ensures that these models have a hidden global tfG symmetry together with a local tfH gauge symmetry.

Supersymmetric WZW Model on Full and Half Plane ; We study classical integrability of the supersymmetric UN sigma model with the WessZuminoWitten term on full and half plane. We demonstrate the existence of nonlocal conserved currents of the model and derive general recursion relations for the infinite number of the corresponding charges in a superfield framework. The explicit form of the first few supersymmetric charges are constructed. We show that the considered model is integrable on full plane as a concequence of the conservation of the supersymmetric charges. Also, we study the model on half plane with free boundary, and examine the conservation of the supersymmetric charges on half plane and find that they are conserved as a result of the equations of motion and the free boundary condition. As a result, the model on half plane with free boundary is integrable. Finally, we conclude the paper and some features and comments are presented.

Type 0A matrix model of black hole, integrability and holography ; We investigate a deformed matrix model of type 0A theory related to supersymmetric Witten's black hole in twodimensions, generalization of bosonic model suggested by Kazakov et. al. We find a free field realization of the partition function of the matrix model, which includes RamondRamond perturbations in the type 0A theory. In a simple case, the partition function is factorized into two determinants, which are given by tau function of an integrable system. We work out the genus expansion of the partition function. Holographic relation with the supersymmetric Witten's black hole is checked by Wilson line computation. Corresponding partition function of the matrix model exhibits a singular behavior, which is interpreted as the point of enhanced cal N2 worldsheet supersymmetry. Interesting relation of the deformed matrix model and topological string on a Z2 orbifold of conifold is found.

Selfduality of d2 Reduction of Gravity Coupled to a SigmaModel ; Dimensional reduction in two dimensions of gravity in higher dimension, or more generally of d3 gravity coupled to a sigmamodel on a symmetric space, is known to possess an infinite number of symmetries. We show that such a bidimensional model can be embedded in a covariant way into a sigmamodel on an infinite symmetric space, built on the semidirect product of an affine group by the Witt group. The finite theory is the solution of a covariant selfduality constraint on the infinite model. It has therefore the symmetries of the infinite symmetric space. We give explicit transformations of the gauge algebra. The usual physical fields are recovered in a triangular gauge, in which the equations take the form of the usual linear systems which exhibit the integrable structure of the models. Moreover, we derive the constraint equation for the conformal factor, which is associated to the central term of the affine group involved.

An Inflaton Mass Problem in String Inflation from Threshold Corrections to Volume Stabilization ; Inflationary models whose vacuum energy arises from a Dterm are believed not to suffer from the supergravity eta problem of Fterm inflation. That is, Dterm models have the desirable property that the inflaton mass can naturally remain much smaller than the Hubble scale. We observe that this advantage is lost in models based on string compactifications whose volume is stabilized by a nonperturbative superpotential the Fterm energy associated with volume stabilization causes the eta problem to reappear. Moreover, any shift symmetries introduced to protect the inflaton mass will typically be lifted by threshold corrections to the volumestabilizing superpotential. Using threshold corrections computed by Berg, Haack, and Kors, we illustrate this point in the example of the D3D7 inflationary model, and conclude that inflation is possible, but only for finetuned values of the stabilized moduli. More generally, we conclude that inflationary models in stable string compactifications, even Dterm models with shift symmetries, will require a certain amount of finetuning to avoid this new contribution to the eta problem.

Partial Supersymmetry Breaking and N2 UNc Gauge Model with Hypermultiplets in Harmonic Superspace ; We provide a manifestly N2 supersymmetric formulation of the N2 UNc gauge model constructed in terms of N1 superfields in hepth0409060. The model is composed of N2 vector multiplets in harmonic superspace and can be viewed as the N2 UNc YangMills effective action equipped with the electric and magnetic FayetIliopoulos terms. We generalize this gauge model to an N2 UNc QCD model by introducing N2 hypermultiplets in harmonic superspace which include both the fundamental representation of UNc and the adjoint representation of UNc. The effect of the magnetic FayetIliopoulos term is to shift the auxiliary field by an imaginary constant. Examining vacua of the model, we show that N2 supersymmetry is spontaneously broken down to N1.

Dual branes in topological sigma models over Lie groups. BFtheory and nonfactorizable Lie bialgebras ; We complete the study of the PoissonSigma model over PoissonLie groups. Firstly, we solve the models with targets G and G the dual group of the PoissonLie group G corresponding to a triangular rmatrix and show that the model over G is always equivalent to BFtheory. Then, given an arbitrary rmatrix, we address the problem of finding Dbranes preserving the duality between the models. We identify a broad class of dual branes which are subgroups of G and G, but not necessarily PoissonLie subgroups. In particular, they are not coisotropic submanifolds in the general case and what is more, we show that by means of duality transformations one can go from coisotropic to noncoisotropic branes. This fact makes clear that noncoisotropic branes are natural boundary conditions for the PoissonSigma model.

Super YangMills Theory from a Supermatrix Model ; It is known that YangMills theories on noncommutative space can be derived from largeN reduced models. Gauge fields in noncommutative YangMills theories can be described as fluctuations of matrices expanded about an appropriate classical solution of the reduced models. We investigate a generalization of this procedure in superfield formalism. We show that we can construct a supermatrix model such that D4 N1 super YangMills theory can be derived from it. In addition, we can couple matter supermatrices to this supermatrix model and also construct models corresponding to N2 and N4 super YangMills theories. In these investigations, we need to introduce a new nonanticommutative superspace, and we investigate the definition of field theories on this space.

An SU5 Heterotic Standard Model ; We introduce a new heterotic Standard Model which has precisely the spectrum of the Minimal Supersymmetric Standard Model MSSM, with no exotic matter. The observable sector has gauge group SU3 x SU2 x U1. Our model is obtained from a compactification of heterotic strings on a CalabiYau threefold with Z2 fundamental group, coupled with an invariant SU5 bundle. Depending on the region of moduli space in which the model lies, we obtain a spectrum consisting of the three generations of the Standard Model, augmented by 0, 1 or 2 Higgs doublet conjugate pairs. In particular, we get the first compactification involving a heterotic string vacuum i.e. a it stable bundle yielding precisely the MSSM with a single pair of Higgs.

Covariant quantization of infinite spin particle models, and higher order gauge theories ; Further properties of a recently proposed higher order infinite spin particle model are derived. Infinitely many classically equivalent but different Hamiltonian formulations are shown to exist. This leads to a condition of uniqueness in the quantization process. A consistent covariant quantization is shown to exist. Also a recently proposed supersymmetric version for halfodd integer spins is quantized. A general algorithm to derive gauge invariances of higher order Lagrangians is given and applied to the infinite spin particle model, and to a new higher order model for a spinning particle which is proposed here, as well as to a previously given higher order rigid particle model. The latter two models are also covariantly quantized.

The open XXZ and associated models at q root of unity ; The generalized open XXZ model at q root of unity is considered. We review how associated models, such as the q harmonic oscillator, and the lattice sineGordon and Liouville models are obtained. Explicit expressions of the local Hamiltonian of the spin 1 over 2 XXZ spin chain coupled to dynamical degrees of freedom at the one end of the chain are provided. Furthermore, the boundary nonlocal charges are given for the lattice sine Gordon model and the q harmonic oscillator with open boundaries. We then identify the spectrum and the corresponding Bethe states, of the XXZ and the q harmonic oscillator in the cyclic representation with special non diagonal boundary conditions. Moreover, the spectrum and Bethe states of the lattice versions of the sineGordon and Liouville models with open diagonal boundaries is examined. The role of the conserved quantities boundary nonlocal charges in the derivation of the spectrum is also discussed.

Nature of the deconfining phase transition in the 21dimensional SUN GeorgiGlashow model ; The nature of the deconfining phase transition in the 21dimensional SUN GeorgiGlashow model is investigated. Within the dimensionalreduction hypothesis, the properties of the transition are described by a twodimensional vectorial Coulomb gas models of electric and magnetic charges. The resulting critical properties are governed by a generalized SUN sineGordon model with selfdual symmetry. We show that this model displays a massless flow to an infrared fixed point which corresponds to the ZN parafermions conformal field theory. This result, in turn, supports the conjecture of Kogan, Tekin, and Kovner that the deconfining transition in the 21dimensional SUN GeorgiGlashow model belongs to the ZN universality class.

On the Null Energy Condition and Cosmology ; Field theories which violate the null energy condition NEC are of interest for the solution of the cosmological singularity problem and for models of cosmological dark energy with the equation of state parameter w1. We discuss the consistency of two recently proposed models that violate the NEC. The ghost condensate model requires higherorder derivative terms in the action. It leads to a heavy ghost field and unbounded energy. We estimate the rates of particles decay and discuss possible mass limitations to protect stability of matter in the ghost condensate model. The nonlocal stringy model that arises from a cubic string field theory and exhibits a phantom behavior also leads to unbounded energy. In this case the spectrum of energy is continuous and there are no particle like excitations. This model admits a natural UV completion since it comes from superstring theory.

Algebraic Geometry over model categories a general approach to derived algebraic geometry ; For a semimodel category M, we define a notion of a ''homotopy'' Grothendieck topology on M, as well as its associated model category of stacks. We use this to define a notion of geometric stack over a symmetric monoidal base model category; geometric stacks are the fundamental objects to do algebraic geometry over model categories. We give two examples of applications of this formalism. The first one is the interpretation of DGschemes as geometric stacks over the model category of complexes and the second one is a definition of etale Ktheory of Einftyring spectra. This first version is very preliminary and might be considered as a detailed research announcement. Some proofs, more details and more examples will be added in a forthcoming version.

Hysteresis phenomenon in deterministic traffic flows ; We study phase transitions of a system of particles on the onedimensional integer lattice moving with constant acceleration, with a collision law respecting slower particles. This simple deterministic particlehopping'' traffic flow model being a straightforward generalization to the well known NagelSchreckenberg model covers also a more recent slowtostart model as a special case. The model has two distinct ergodic unmixed phases with two critical values. When traffic density is below the lowest critical value, the steady state of the model corresponds to the freeflowing'' or gaseous'' phase. When the density exceeds the second critical value the model produces large, persistent, welldefined traffic jams, which correspond to the jammed'' or liquid'' phase. Between the two critical values each of these phases may take place, which can be interpreted as an overcooled gas'' phase when a small perturbation can change drastically gas into liquid. Mathematical analysis is accomplished in part by the exact derivation of the lifetime of individual traffic jams for a given configuration of particles.

Individualbased probabilistic models of adaptive evolution and various scaling approximations ; We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population of discrete individuals characterized by one or several adaptive traits. The population is modelled as a stochastic point process whose generator captures the probabilistic dynamics over continuous time of birth, mutation, and death, as influenced by each individual's trait values, and interactions between individuals. An offspring usually inherits the trait values of her progenitor, except when a mutation causes the offspring to take an instantaneous mutation step at birth to new trait values. We look for tractable large population approximations. By combining various scalings on population size, birth and death rates, mutation rate, mutation step, or time, a single microscopic model is shown to lead to contrasting macroscopic limits, of different nature deterministic, in the form of ordinary, integro, or partial differential equations, or probabilistic, like stochastic partial differential equations or superprocesses. In the limit of rare mutations, we show that a possible approximation is a jump process, justifying rigorously the socalled trait substitution sequence. We thus unify different points of view concerning mutationselection evolutionary models.

Enriched model categories and an application to additive endomorphism spectra ; We define the notion of an additive model category, and we prove that any additive, stable, combinatorial model category has a natural enrichment over symmetric spectra based on simplicial abelian groups. As a consequence, every object in such a model category has a naturally associated endomorphism ring inside this spectra category. We establish the basic properties of this enrichment. We also develop some enriched model category theory. In particular, we have a notion of an adjoint pair of functors being a 'module' over another such pair. Such things are called adjoint modules. We develop the general theory of these, and use them to prove a result about transporting enrichments over one symmetric monoidal model category to a Quillen equivalent one.

Asymptotic theorems of sequential estimationadjusted urn models ; The Generalized P'olya Urn GPU is a popular urn model which is widely used in many disciplines. In particular, it is extensively used in treatment allocation schemes in clinical trials. In this paper, we propose a sequential estimationadjusted urn model a nonhomogeneous GPU which has a wide spectrum of applications. Because the proposed urn model depends on sequential estimations of unknown parameters, the derivation of asymptotic properties is mathematically intricate and the corresponding results are unavailable in the literature. We overcome these hurdles and establish the strong consistency and asymptotic normality for both the patient allocation and the estimators of unknown parameters, under some widely satisfied conditions. These properties are important for statistical inferences and they are also useful for the understanding of the urn limiting process. A superior feature of our proposed model is its capability to yield limiting treatment proportions according to any desired allocation target. The applicability of our model is illustrated with a number of examples.

Quantitative Neron theory for torsion bundles ; Let R be a discrete valuation ring with algebraically closed residue field, and consider a smooth curve CK over the field of fractions K. For any positive integer r prime to the residual characteristic, we consider the finite Kgroup scheme PicCKr of rtorsion line bundles on CK. We determine when there exists a finite Rgroup scheme, which is a model of PicCKr over R; in other words, we establish when the N'eron model of PicCKr is finite. To this effect, one needs to analyse the points of the N'eron model over R, which, in general, do not represent rtorsion line bundles on a semistable reduction of CK. Instead, we recast the notion of models on a stacktheoretic base there, we find finite N'eron models, which represent rtorsion line bundles on a stacktheoretic semistable reduction of CK. This allows us to quantify the lack of finiteness of the classical N'eron models and finally to provide an efficient criterion for it.

The conjugate prior for discrete hierarchical loglinear models ; In the Bayesian analysis of contingency table data, the selection of a prior distribution for either the loglinear parameters or the cell probabilities parameter is a major challenge. Though the conjugate prior on cell probabilities has been defined by Dawid and Lauritzen 1993 for decomposable graphical models, it has not been identified for the larger class of graphical models Markov with respect to an arbitrary undirected graph or for the even wider class of hierarchical loglinear models. In this paper, working with the loglinear parameters used by GLIM, we first define the conjugate prior for these parameters and then derive the induced prior for the cell probabilities this is done for the general class of hierarchical loglinear models. We show that the conjugate prior has all the properties that one expects from a prior notational simplicity, ability to reflect either no prior knowledge or a priori expert knowledge, a moderate number of hyperparameters and mathematical convenience. It also has the strong hyper Markov property which allows for local updates within prime components for graphical models.

Construction of Kink Sectors for TwoDimensional Quantum Field Theory Models. An Algebraic Approach ; Several twodimensional quantum field theory models have more than one vacuum state. Familiar examples are the SineGordon and the phi42model. It is known that in these models there are also states, called kink states, which interpolate different vacua. A general construction scheme for kink states in the framework of algebraic quantum field theory is developed in a previous paper. However, for the application of this method, the crucial condition is the split property for wedge algebras in the vacuum representations of the considered models. It is believed that the vacuum representations of Pphi2models fulfill this condition, but a rigorous proof is only known for the massive free scalar field. Therefore, we investigate in a construction of kink states which can directly be applied to a large class of quantum field theory models, by making use of the properties of the dynamics of a Pphi2 and Yukawa2 models.

The Phase Transition in Statistical Models Defined on Farey Fractions ; We consider several statistical models defined on the Farey fractions. Two of these models may be regarded as spin chains, with longrange interactions, while another arises in the study of multifractals associated with chaotic maps exhibiting intermittency. We prove that these models all have the same free energy. Their thermodynamic behavior is determined by the spectrum of the transfer operator RuellePerronFrobenius operator, which is defined using the maps presentation functions generating the Farey tree. The spectrum of this operator was completely determined by Prellberg. It follows that these models have a secondorder phase transition with a specific heat divergence of the form t ln t21. The spin chain models are also rigorously known to have a discontinuity in the magnetization at the phase transition.

Equivalence of the super Lax and local Dunkl operators for Calogerolike models ; Following Shastry and Sutherland I construct the super Lax operators for the Calogero model in the oscillator potential. These operators can be used for the derivation of the eigenfunctions and integrals of motion of the Calogero model and its supersymmetric version. They allow to infer several relations involving the Lax matrices for this model in a fast way. It is shown that the super Lax operators for the Calogero and Sutherland models can be expressed in terms of the supercharges and so called local Dunkl operators constructed in our recent paper with M. Ioffe. Several important relations involving Lax matrices and Hamiltonians of the Calogero and Sutherland models are easily derived from the properties of Dunkl operators.

On Gibbs Measures of Models with Competing Ternary and Binary Interactions and Corresponding Von Neumann Algebras II ; In the present paper the Ising model with competing binary J and binary J1 interactions with spin values pm 1, on a Cayley tree of order 2 is considered. The structure of Gibbs measures for the model considered is studied. We completely describe the set of all periodic Gibbs measures for the model with respect to any normal subgroup of finite index of a group representation of the Cayley tree. Types of von Neumann algebras, generated by GNSrepresentation associated with diagonal states corresponding to the translation invariant Gibbs measures, are determined. It is proved that the factors associated with minimal and maximal Gibbs states are isomorphic, and if they are of type IIIlambda then the factor associated with the unordered phase of the model can be considered as a subfactors of these factors respectively. Some concrete examples of factors are given too. 10mm bf Keywords Cayley tree, Ising model, competing interactions, Gibbs measure, GNSconstruction, Hamiltonian, von Neumann algebra.

Transition from coherence to bistability in a model of financial markets ; We present a model describing the competition between information transmission and decision making in financial markets. The solution of this simple model is recalled, and possible variations discussed. It is shown numerically that despite its simplicity, it can mimic a size effect comparable to a crash. Two extensions of this model are presented that allow to simulate the demand process. One of these extensions has a coherent stable equilibrium and is selforganized, while the other has a bistable equilibrium, with a spontaneous segregation of the population of agents. A new model is introduced to generate a transition between those two equilibriums. We show that the coherent state is dominant up to an equal mixing of the two extensions. We focuss our attention on the microscopic structure of the investment rate, which is the main parameter of the original model. A constant investment rate seems to be a very good approximation.

A Simple Model of Epidemics with Pathogen Mutation ; We study how the interplay between the memory immune response and pathogen mutation affects epidemic dynamics in two related models. The first explicitly models pathogen mutation and individual memory immune responses, with contacted individuals becoming infected only if they are exposed to strains that are significantly different from other strains in their memory repertoire. The second model is a reduction of the first to a system of difference equations. In this case, individuals spend a fixed amount of time in a generalized immune class. In both models, we observe four fundamentally different types of behavior, depending on parameters 1 pathogen extinction due to lack of contact between individuals, 2 endemic infection 3 periodic epidemic outbreaks, and 4 one or more outbreaks followed by extinction of the epidemic due to extremely low minima in the oscillations. We analyze both models to determine the location of each transition. Our main result is that pathogens in highly connected populations must mutate rapidly in order to remain viable.

Q4 ; One of the most fascinating and technically demanding parts of the theory of twodimensional integrable systems constitute the models with the spectral parameter on an elliptic curve, including LandauLifshitz and KricheverNovikov equations, as well as elliptic Toda and RuijsenaarsToda lattices, elliptic Volterra lattice and ShabatYamilov lattice. We explain how all these models can be unified on the basis of a single equation Q4 on a quadgraph. This discrete model plays the role of the master equation'' in the sl2 part of 2D integrability most of other models in this area can be obtained from this one by certain limiting procedures. More precisely, discrete versions of all of the above mentioned models appear from Q4 imposed on a multidimensional cubic lattice. Zero curvature representations for all models appear as a byproduct of the general construction.

Mathematical Models of Bipolar Disorder ; We use limit cycle oscillators to model Bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about one percent of the United States adult population. We consider two nonlinear oscillator models of a single bipolar patient. In both frameworks, we begin with an untreated individual and examine the mathematical effects and resulting biological consequences of treatment. We also briefly consider the dynamics of interacting bipolar II individuals using weaklycoupled, weaklydamped harmonic oscillators. We discuss how the proposed models can be used as a framework for refined models that incorporate additional biological data. We conclude with a discussion of possible generalizations of our work, as there are several biologicallymotivated extensions that can be readily incorporated into the series of models presented here.

Discrete KleinGordon models with static kinks free of the PeierlsNabarro potential ; For the nonlinear KleinGordon type models, we describe a general method of discretization in which the static kink can be placed anywhere with respect to the lattice. These discrete models are therefore free of the it static PeierlsNabarro potential. Previously reported models of this type are shown to belong to a wider class of models derived by means of the proposed method. A relevant physical consequence of our findings is the existence of a wide class of discrete KleinGordon models where slow kinks it practically do not experience the action of the PeierlsNabarro potential. Such kinks are not trapped by the lattice and they can be accelerated by even weak external fields.

SU3 RichardsonGaudin models three level systems ; We present the exact solution of the RichardsonGaudin models associated with the SU3 Lie algebra. The derivation is based on a Gaudin algebra valid for any simple Lie algebra in the rational, trigonometric and hyperbolic cases. For the rational case additional cubic integrals of motion are obtained, whose number is added to that of the quadratic ones to match, as required from the integrability condition, the number of quantum degrees of freedom of the model. We discuss different SU3 physical representations and elucidate the meaning of the parameters entering in the formalism. By considering a bosonic mapping limit of one of the SU3 copies, we derive new integrable models for three level systems interacting with two bosons. These models include a generalized TavisCummings model for three level atoms interacting with two modes of the quantized electric field.

Scaling Behavior in Soliton Models ; In the framework of chiral soliton models we study the behavior of static nucleon properties under rescaling of the parameters describing the effective meson theory. In particular we investigate the question of whether the BrownRho scaling laws are general features of such models. When going beyond the simple Skyrme model we find that restrictive constraints need to be imposed on the mesonic parameters in order to maintain these scaling laws. Furthermore, in the case when vector mesons are included in the model it turns out that the isoscalar form factor no longer scales according to these laws. Finally we note that, in addition to the exact scaling laws of the model, one may construct approximate it local scaling laws, which depend of the particular choice of Lagrangian parameters.

The damping width of giant dipole resonances of cold and hot nuclei a macroscopic model ; A phenomenological macroscopic model of the Giant Dipole Resonance GDR damping width of cold and hotnuclei with groundstate spherical and nearspherical shapes is developed. The model is based on a generalized Fermi Liquid model which takes into account the nuclear surface dynamics. The temperature dependence of the GDR damping width is accounted for in terms of surface and volumecomponents. Parameterfree expressions for the damping width and the effective deformation are obtained. The model is validated with GDR measurements of the following nuclides, 39,40K, 42Ca, 45Sc, 59,63Cu, 109120Sn,147Eu, 194Hg, and 208Pb, and is compared with the predictions of other models.

A Particle Model of Rolling Grain Ripples Under Waves ; A simple model is presented for the formation of rolling grain ripples on a flat sand bed by the oscillatory flow generated by a surface wave. An equation of motion is derived for the individual ripples, seen as particles, on the otherwise flat bed. The model account for the initial apperance of the ripples, the subsequent coarsening of the ripples and the final equilibrium state. The model is related to physical parameters of the problem, and an analytical approximation for the equilibrium spacing of the ripples is developed. It is found that the spacing between the ripples scale with the squareroot of the nondimensional shear stress the Shields parameter on a flat bed. The results of the model are compared with measurements, and reasonable agreement between the model and the measurements is demonstrated.

A Simple Model of Evolution with Variable System Size ; A simple model of biological extinction with variable system size is presented that exhibits a powerlaw distribution of extinction event sizes. The model is a generalization of a model recently introduced by Newman Proc. R. Soc. Lond. B265, 1605 1996. Both analytical and numerical analysis show that the exponent of the powerlaw distribution depends only marginally on the growth rate g at which new species enter the system and is equal to the one of the original model in the limit gtoinfty. A critical growth rate gc can be found below which the system dies out. Under these model assumptions stable ecosystems can only exist if the regrowth of species is sufficiently fast.

The distribution of wealth in the presence of altruism for simple economic models ; We study the effect of altruism in two simple asset exchange models the yard sale model winner gets a random fraction of the poorer player's wealth and the theft and fraud model winner gets a random fraction of the loser's wealth. We also introduce in these models the concept of bargaining efficiency, which makes the poorer trader more aggressive in getting a favorable deal thus augmenting his winning probabilities. The altruistic behavior is controlled by varying the number of traders that behave altruistically and by the degree of altruism that they show. The resulting wealth distribution is characterized using the Gini index. We compare the resulting values of the Gini index at different levels of altruism in both models. It is found that altruistic behavior does lead to a more equitable wealth distribution but only for unreasonable high values of altruism that are difficult to expect in a real economic system.

Ordering dynamics with two nonexcluding options Bilingualism in language competition ; We consider a modification of the voter model in which a set of interacting elements agents can be in either of two equivalent states A or B or in a third additional mixed AB state. The model is motivated by studies of language competition dynamics, where the AB state is associated with bilingualism. We study the ordering process and associated interface and coarsening dynamics in regular lattices and small world networks. Agents in the AB state define the interfaces, changing the interfacial noise driven coarsening of the voter model to curvature driven coarsening. We argue that this change in the coarsening mechanism is generic for perturbations of the voter model dynamics. When interaction is through a small world network the AB agents restore coarsening, eliminating the metastable states of the voter model. The time to reach the absorbing state scales with system size as tau sim ln N to be compared with the result tau sim N for the voter model in a small world network.

Quantumlike Probabilistic Models outside Physics ; We present a quantumlike QL model in that contexts complexes of e.g. mental, social, biological, economic or even political conditions are represented by complex probability amplitudes. This approach gives the possibility to apply the mathematical quantum formalism to probabilities induced in any domain of science. In our model quantum randomness appears not as irreducible randomness as it is commonly accepted in conventional quantum mechanics, e.g., by von Neumann and Dirac, but as a consequence of obtaining incomplete information about a system. We pay main attention to the QL description of processing of incomplete information. Our QL model can be useful in cognitive, social and political sciences as well as economics and artificial intelligence. In this paper we consider in a more detail one special application QL modeling of brain's functioning. The brain is modeled as a QLcomputer.

Complementarity principle on human longevity ; In recent we introduced, developed and established a new concept, model, methodology and principle for studying human longevity in terms of demographic basis. We call the new model the Weon model, which is a general model modified from the Weibull model with an agedependent shape parameter to describe human survival and mortality curves. We demonstrate the application of the Weon model to the mortality dynamics and the mathematical limit of longevity the mortality rate to be mathematically zero, implying a maximum longevity in the Section I. The mathematical limit of longevity can be induced by the mortality dynamics in nature. As a result, we put forward the complementarity principle, which explains the recent paradoxical trends that the mathematical limit decreases as the longevity increases, in the Section II. Our findings suggest that the human longevity can be limited by the complementarity principle.

Statistical model selection methods applied to biological networks ; Many biological networks have been labelled scalefree as their degree distribution can be approximately described by a powerlaw distribution. While the degree distribution does not summarize all aspects of a network it has often been suggested that its functional form contains important clues as to underlying evolutionary processes that have shaped the network. Generally determining the appropriate functional form for the degree distribution has been fitted in an adhoc fashion. Here we apply formal statistical model selection methods to determine which functional form best describes degree distributions of protein interaction and metabolic networks. We interpret the degree distribution as belonging to a class of probability models and determine which of these models provides the best description for the empirical data using maximum likelihood inference, composite likelihood methods, the Akaike information criterion and goodnessoffit tests. The whole data is used in order to determine the parameter that best explains the data under a given model e.g. scalefree or random graph. As we will show, present protein interaction and metabolic network data from different organisms suggests that simple scalefree models do not provide an adequate description of real network data.

The use of the GARP genetic algorithm and internet grid computing in the Lifemapper world atlas of species biodiversity ; Lifemapper httpwww.lifemapper.org is a predictive electronic atlas of the Earth's biological biodiversity. Using a screensaver version of the GARP genetic algorithm for modeling species distributions, Lifemapper harnesses vast computing resources through 'volunteers' PCs similar to SETIhome, to develop models of the distribution of the worlds fauna and flora. The Lifemapper project's primary goal is to provide an up to date and comprehensive database of species maps and prediction models i.e. a fauna and flora of the world using available data on species' locations. The models are developed using specimen data from distributed museum collections and an archive of geospatial environmental correlates. A central server maintains a dynamic archive of species maps and models for research, outreach to the general community, and feedback to museum data providers. This paper is a case study in the role, use and justification of a genetic algorithm in development of largescale environmental informatics infrastructure.

Gompertz mortality law and scaling behaviour of the Penna model ; The Penna model is a model of evolutionary ageing through mutation accumulation where traditionally time and the age of an organism are treated as discrete variables and an organism's genome by a binary bit string. We reformulate the asexual Penna model and show that, a universal scale invariance emerges as we increase the number of discrete genome bits to the limit of a continuum. The continuum model, introduced by Almeida and Thomas in Int.J.Mod.Phys.C, 11, 1209 2000 can be recovered from the discrete model in the limit of infinite bits coupled with a vanishing mutation rate per bit. Finally, we show that scale invariant properties may lead to the ubiquitous Gompertz Law for mortality rates for early ages, which is generally regarded as being empirical.

When does division of labor lead to increased system output ; This paper develops a set of simplified dynamical models with which to explore the conditions under which division of labor leads to optimized system output, as measured by the rate of production of a given product. We consider two models In the first model, we consider the flow of some resource into a compartment, and the conversion of this resource into some product. In the second model, we consider the resourcelimited growth of autoreplicating systems. In this case, we divide the replication and metabolic tasks among different agents. The general features that emerge from our models is that division of labor is favored when the resource to agent ratio is at intermediate values, and when the time cost associated with transporting intermediate products is small compared to characteristic process times. We discuss the results of this paper in the context of simulations with digital life. We also argue that division of labor in the context of our replication model suggests an evolutionary basis for the emergence of the stemcellbased tissue architecture in complex organisms.

Modelling Sex Ratio and Numbers for Translocation in MetaPopulation Management ; The management of endangered species as metapopulations is becoming increasingly common. Diverse aspects of metapopulation dynamics and management have received attention in recent years. In particular, translocation of individuals between subpopulations of a metapopulation is practiced, or envisaged, for a variety of reasons and requires careful consideration. Linklater 2003 proposed that the number of individuals of each sex translocated into a target population for the purposes of maintaining genetic diversity could be chosen on the basis of parental investment theory. In this paper, following basic ideas in the parental investment literature, I propose a simple model to capture Linklater's proposal and provide a thorough mathematical analysis of the model. Granted the necessary speciesspecific biological information which would determine the model parameters in any instance of application, the analysis indicates that a practical algorithm can be constructed to generate the model's predictions for the optimal translocation.