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A Note on Orientifolds and Dualities of Type 0B String Theory ; We generalize the construction of four dimensional nontachyonic orientifolds of type 0B string theory to nonsupersymmetric backgrounds. We construct a four dimensional model containing selfdual D3 and D9branes and leading to a chiral anomalyfree massless spectrum. Moreover, we discuss a further tachyonfree six dimensional model with only D5 branes. Eventually, we speculate about strong coupling dual models of the tendimensional orientifolds of type 0B.

An SL2,R Model of Constrained Systems Algebraic Constraint Quantization ; A reparametrization invariant model, introduced by Montesinos, Rovelli and Thiemann, possessing an SL2,R gauge symmetry is treated along the guidelines of an algebraic constraint quantization scheme that translates the vanishing of the constraints into representation conditions for the algebra of observables. The application of this algebraic scheme to the SL2,R model yields an unambiguous identification of the physical representation of the algebra of observables.

The Schrodinger Representation for Fermions and a Local Expansion of the Schwinger Model ; We discuss the functional representation of fermions, and obtain exact expressions for wavefunctionals of the Schwinger model. Known features of the model such as bosonization and the vacuum angle arise naturally. Contrary to expectations, the vacuum wavefunctional does not simplify at large distances, but it may be reconstructed as a large time limit of the corresponding Schrodinger functional, which has an expansion in local terms. The functional Schrodinger equation reduces to a set of algebraic equations for the coefficients of these terms. These ideas generalize to a numerical approach to QCD in higher dimensions.

Path integral quantization of the PoissonSigma model ; We apply the antifield quantization method of Batalin and Vilkovisky to the calculation of the path integral for the PoissonSigma model in a general gauge. For a linear Poisson structure the model reduces to a nonabelian gauge theory, and we obtain the formula for the partition function of twodimensional YangMills theory for closed twodimensional manifolds.

Gauged Thirring Model in the Heisenberg Picture ; We consider the 21dimensional gauged Thirring model in the Heisenberg picture. In this context we evaluate the vacuum polarization tensor as well as the corrected gauge boson propagator and address the issues of generation of mass and dynamics for the gauge boson in the limits of QED3 and Thirring model as a gauge theory, respectively due to the radiative corrections.

PoissonSigma Models ; We investigate the PoissonSigma model on the classical and quantum level. In the classical analysis we show how this model includes various known twodimensional field theories. Then we perform the calculation of the path integral in a general gauge, and demonstrate that the derived partition function reduces to the familiar form in the case of 2d YangMills theory.

Torsionless Tselfdual Affine NA Toda Models ; A general construction of affine Non Abelian Toda models in terms of gauged two loop WZNW model is discussed. In particular we find the Lie algebraic condition defining a subclass of it Tselfdual torsionless NA Toda models and their zero curvature representation.

Mirror Symmetry ; We prove mirror symmetry for supersymmetric sigma models on Kahler manifolds in 11 dimensions. The proof involves establishing the equivalence of the gauged linear sigma model, embedded in a theory with an enlarged gauge symmetry, with a LandauGinzburg theory of Toda type. Standard R 1R duality and dynamical generation of superpotential by vortices are crucial in the derivation. This provides not only a proof of mirror symmetry in the case of local and global CalabiYau manifolds, but also for sigma models on manifolds with positive first Chern class, including deformations of the action by holomorphic isometries.

Inflationary Universe in Higher Derivative Induced Gravity ; In an inducedgravity model, the stability condition of an inflationary slowrollover solution is shown to be phi0 partialphi0Vphi04Vphi0. The presence of higher derivative terms will, however, act against the stability of this expanding solution unless further constraints on the field parameters are imposed. We find that these models will acquire a nonvanishing cosmological constant at the end of inflation. Some models are analyzed for their implication to the early universe.

Lectures on the Microscopic Modeling of the 5dim. Black Hole of IIB String Theory and the D1D5 System ; In these notes we review the theory of the microscopic modeling of the 5dim. black hole of type IIB string theory in terms of the D1D5 brane system. The emphasis here is more on the brane dynamics rather than on supergravity solutions. We present a discussion of the low energy brane dynamics and account for black hole thermodynamics and Hawking radiation rates. These considerations are valid in the regime of supergravity due to the nonrenormalization of the low energy dynamics in this model.

On the Equivalence of Noncommutative Models in Various Dimensions and Brane Condensation ; Here we construct a map from the algebra of fields in twodimensional noncommutative of U1 YangMills fields interacting with KaluzaKlein scalars to a Ddimensional one, as a solution in the twodimensional model. This proves the equivalence of noncommutative models in various even dimensions. Physically this map describes condensation of D1branes.

Boundary spectrum in the sineGordon model with Dirichlet boundary conditions ; We find the spectrum of boundary bound states for the sineGordon model with Dirichlet boundary conditions, closing the bootstrap and providing a complete description of all the poles in the boundary reflection factors. The boundary ColemanThun mechanism plays an important role in the analysis. Two basic lemmas are introduced which should hold for any 11dimensional boundary field theory, allowing the general method to be applied to other models.

Gauge models in modified triplectic quantization ; We apply the modified triplectic formalism for quantizing several popular gauge models nonabelian antisymmetric tensor field model, W2gravity and twodimensional gravity with dynamical torsion. The explicit solutions are obtained for the generating equations of the quantum action and the gaugefixing functional. Using these solutions we construct the vacuum functional and obtain the corresponding transformations of the extended BRST symmetry.

Topologically massive nonabelian BF models in arbitrary spacetime dimensions ; This work extends to the Ddimensional spacetime the topological mass generation mechanism of the nonabelian BF model in four dimensions. In order to construct the gauge invariant nonabelian kinetic terms for a D2form B and a 1form A, we introduce an auxiliary D3form V. Furthermore, we obtain a complete set of BRST and antiBRST transformation rules of the fields using the so called horizontality condition, and construct a BRSTantiBRST invariant quantum action for the model in Ddimensional spacetime.

Scale Invariance in a NonAbelian ChernSimonsMatter Model ; The general method of reduction in the number of coupling parameters is applied in a ChernSimonsmatter model with several independent couplings. We claim that considering the asymptotic region, and expressing all dimensionless coupling parameters as functions of the ChernSimons coupling, it is possible to show that all betafunctions vanish to any order of perturbative series. Therefore, the model is asymptotically scale invariant.

The global phase diagram of a modular invariant two dimensional statistical model ; A generalization of the Coulomb Gas model with modular SL2, Zsymmetry allows for a discrete infinity of phases which are characterized by the condensation of dyonic pseudoparticles and the breaking of parity and time reversal. Here we study the phase diagram of such a model by using renormalization group techniques. Then the symmetry SL2,Z acting on the twodimensional parameter space gives us a nested shape of its global phase diagram and all the infrared stable fixed points. Finally we propose a connection with the 2dimensional Conformal Field Theory description of the Fractional Quantum Hall Effect.

A practical gauge invariant regularization of the SO10 grand unified model ; It is shown that a simple modification of the dimensional regularization allows to compute in a consistent and gauge invariant way any diagram with less than four loops in the SO10 unified model. The method applies also to the Standard Model generated by the symmetry breaking SO10 to SU3times SU2times U1. A gauge invariant regularization for arbitrary diagram is also described.

Consistent superconformal boundary states ; We propose a supersymmetric generalization of Cardy's equation for consistent N1 superconformal boundary states. We solve this equation for the superconformal minimal models SMpp2 with p odd, and thereby provide a classification of the possible superconformal boundary conditions. In addition to the NeveuSchwarz NS and Ramond R boundary states, there are NS states. The NS and NS boundary states are related by a Z2 spinreversal transformation. We treat the tricritical Ising model as an example, and in an appendix we discuss the nonsuperconformal case of the Ising model.

On Stability Of The Crystal Universe Models ; We generalize the GoldbergerWise mechanism and study the stability of the Crystal Universe models. We show that the model can be stabilized, however for configurations of Crystal Universe in the absence of finetuning, brane crystals are not equidistant, i.e. a pair is far away from adjacent pair, except for the fixed points of the orbifold, which differs from the assumptions taken in the literature.

On a CFT prediction in the sineGordon model ; A quantitative prediction of Conformal Field Theory CFT, which relates the second moment of the energydensity correlator away from criticality to the value of the central charge, is verified in the sineGordon model. By exploiting the bosonfermion duality of twodimensional field theories, this result also allows to show the validity of the prediction in the strong coupling regime of the Thirring model.

Finite Noncommutative ChernSimons with a Wilson Line and the Quantum Hall Effect ; We present a finite dimensional matrix model associated to the noncommutative ChernSimons theory, obtained by inserting a Wilson line. For a specific choice of the representation of the Wilson line the model is equivalent to the minimal modification of the matrix model which is compatible with finite dimensional matrices, and was introduced previously to study droplets of quantum Hall fluid. For other representations we obtain generalizations corresponding to regularized Un ChernSimons theoris, representing multilayered quantum Hall fluids.

Lorentzian 3d Gravity with Wormholes via Matrix Models ; We uncover a surprising correspondence between a nonperturbative formulation of threedimensional Lorentzian quantum gravity and a hermitian twomatrix model with ABABinteraction. The gravitational transfer matrix can be expressed as the logarithm of a twomatrix integral, and we deduce from the known structure of the latter that the model has two phases. In the phase of weak gravity, welldefined twodimensional universes propagate in proper time, whereas in the strongcoupling phase the spatial hypersurfaces disintegrate into many components connected by wormholes.

Matrix Model for De Sitter ; Based on a heuristic boost argument, we propose that the 4 dimensional de Sitter space can be described by a spherical ChernSimons matrix model near the cosmological horizon, or models generalizing this simple choice. The dimension of the Hilbert space is naturally finite. We also make some comments on possible realization of holography in this approach, and on possible relation to the conformal field theory approach.

On Lie point symmetry of classical WessZuminoWitten model ; We perform the group analysis of Witten's equations of motion for a particle moving in the presence of a magnetic monopole, and also when constrained to move on the surface of a sphere, which is the classical WessZuminoWitten model. We also consider variations of this model. Our analysis gives the generators of the corresponding Lie point symmetries. The Lie symmetry corresponding to Kepler's third law is obtained in two related examples.

Second order quantum corrections to the classical reflection factor of the sinhGordon model ; The sinhGordon model on a halfline with integrable boundary conditions is considered in low order perturbation theory developed in affine Toda field theory. The quantum corrections to the classical reflection factor of the model are studied up to the second order in the difference of the two boundary parameters and to one loop order in the bulk coupling. It is noticed that the general form of the second order quantum corrections are consistent with Ghoshal's formula.

YangMills Matrix Theory ; We discuss bosonic and supersymmetric YangMills matrix models with compact semisimple gauge group. We begin by finding convergence conditions for the partition and correlation functions. Moving on, we specialise to the SUN models with large N. In both the YangMills and cohomological formulations, we find all quantities which are invariant under the supercharges. Finally, we apply the deformation method of Moore, Nekrasov and Shatashvili directly to the YangMills model. We find a deformation of the action which generates mass terms for all the matrix fields whilst preserving some supersymmetry. This allows us to rigorously integrate over a BRST quartet and arrive at the well known formula of MNS.

On the Integrability of Classical RuijsenaarsSchneider Model of BC2 Type ; The problem of finding most general form of the classical integrable relativistic models of manybody interaction of the BCn type is considered. In the simplest nontrivial case of n2,the extra integral of motion is presented in explicit form within the ansatz similar to the nonrelativistic CalogeroMoser models. The resulting Hamiltonian has been found by solving the set of two functional equations.

On Orientifolds of WZW Models and their Relation to Geometry ; We investigate Dbranes in orientifolds of WZW models. A connection between the conformal field theory approach to orientifolds and the target space motivated analysis is established. In particular, we associate previously constructed crosscap states to involutions of the group manifold and their fixed point sets. Whereas our analysis of Dbranes in orientifolds of general WZW models is restricted to special D0branes, we investigate all symmetry preserving branes of SU2orientifolds in detail. For that case, the location of the orientifold fixed point set is independently determined by scattering localized graviton wave packets.

Thick brane world model from perfect fluid ; A 1 ddimensional thick brane world model with varying Lambdaterm is considered. The model is generalized to the case of a chain of Ricciflat internal spaces when the matter source is an anisotropic perfect fluid. The horizontal part of potential is obtained in the Newtonian approximation. In the multitemporal case with a Lambdaterm a set of equations for potentials is presented.

Dirac Neutrino Masses in NCG ; Several models in NCG with mild changes to the standard modelSMare introduced to discuss the neutrino mass problem. We use two constraints, Poincaracutee duality and gauge anomaly free, to discuss the possibility of containing righthanded neutrinos in them. Our work shows that no model in this paper, with each generation containing a righthanded neutrino, can satisfy these two constraints in the same time. So, to consist with neutrino oscillation experiment results, maybe fundamental changes to the present version of NCG are usually needed to include Dirac massive neutrinos.

SU3X SU2XU1 Chiral Models from Intersecting D4D5branes ; We clarify RR tadpole cancellation conditions for intersecting D4D5branes. We find all of the D4brane models which have D4 threegeneration chiral fermions with the SU3XSU2XU1n symmetries. For the D5brane case, we present a solution to the conditions which gives exactly the matter contents of standard model with U1 anomalies.

Some Considerations Regarding LorentzViolating Theories ; We investigate the compatibility of Lorentzviolating quantum field theories with the requirements of causality and stability. A general renormalizable model for free massive fermions indicates that these requirements are satisfied at low energies provided the couplings controlling the breaking are small. However, for high energies either microcausality or energy positivity or both are violated in some observer frame. We find evidence that this difficulty can be avoided if the model is interpreted as a subPlanckian approximation originating from a nonlocal theory with spontaneous Lorentz violation. The present study thereby supports the validity of the standardmodel extension as the lowenergy limit of any realistic string theory that exhibits spontaneous Lorentz breaking.

Gravitational Waves in Brane World A Midisuperspace Approach ; It is important to reveal the branebulk correspondence for understanding the brane world cosmology. When gravitational waves exist in the bulk, however, it is difficult to make the analysis of the interrelationship between the brane and the bulk. Hence, the minimal model which allows gravitational waves in the bulk would be useful. As for such models, we adopt the Bianchi type midisuperspace models. In particular, the effects of gravitational waves in the bulk on the brane cosmology is examined using the midisuperspace approach.

Noncommutative Gravity in two Dimensions ; We deform twodimensional topological gravity by making use of its gauge theory formulation. The obtained noncommutative gravity model is shown to be invariant under a class of transformations that reduce to standard diffeomorphisms once the noncommutativity parameter is set to zero. Some solutions of the deformed model, like fuzzy AdS2, are obtained. Furthermore, the transformation properties of the model under the SeibergWitten map are studied.

The space of signed points and the Self Dual Model ; We study a generalization of the group of loops based on sets of signed points, instead of paths or loops. This geometrical setting incorporates the kinematical constraints of the Sigma Model, inasmuch as the the group of loops does with the Bianchi identities of YangMills theories. We employ an Abelian version of this construction to quantize the SelfDual Model, which allows us to relate this theory with that of a massless scalar field obeying nontrivial boundary conditions.

Thermodynamics of the critical RSOSq1, q2 ;q model ; The thermodynamic Bethe ansatz method is employed for the study of the integrable critical RSOSq1, q2;q model. The high and low temperature behavior are investigated, and the central charge of the effective conformal field theory is derived. The obtained central charge is expressed as the sum of the central charges of two generalized coset models.

Tadpole Analysis of Orientifolded PlaneWaves ; We study orientifolds of type IIB string theory in the planewave background supported by null RR 3form flux F3. We describe how to extract the RR tadpoles in the GreenSchwarz formalism in a general setting. Two models with orientifold groups 1, Omega and 1,Omega I4, which are Tdual to each other, are considered. Consistency of these backgrounds requires 32 D9 branes for the first model and 32 D5 branes for the second one. We study the spectra and comment on the heterotic duals of our models.

Photon fields in a fluctuating spacetime ; We present a model of interacting quantum fields, formulated in a nonperturbative manner. One of the fields is treated semiclassically, the other is the photon field. The model has an interpretation of an electromagnetic field in a fluctuating spacetime. The model is equivalent with the quantization of electromagnetism proposed recently by Czachor. Interesting features are that standard photon theory is recovered as a limiting case, and that localized field operators for the electromagnetic field exist as unbounded operators in Hilbert space.

Seiberg Duality in Matrix Models II ; In this paper we continue the investigation, within the context of the DijkgraafVafa Programme, of Seiberg duality in matrix models as initiated in hepth0211202, by allowing degenerate mass deformations. In this case, there are some massless fields which remain and the theory has a moduli space. With this illustrative example, we propose a general methodology for performing the relevant matrix model integrations and addressing the corresponding field theories which have nontrivial IR behaviour, and which may or may not have treelevel superpotentials.

Axial Vector Duality in Affine NA Toda Models ; A general and systematic construction of Non Abelian affine Toda models and its symmetries is proposed in terms of its underlying Lie algebraic structure. It is also shown that such class of two dimensional integrable models naturally leads to the construction of a pair of actions related by Tduality transformations

Quantum field fluctuations and chaotic dynamics of model YangMills system ; On example of the model field system we demonstrate that quantum fluctuations of nonabelian gauge fields leading to radiative corrections to Higgs potential and spontaneous symmetry breaking can generate order region in phase space of inherently chaotic classical field system. We demonstrate on the example of another model field system that quantum fluctuations do not influence on the chaotic dynamics of nonabelian YangMills fields if the ratio of bare coupling constants of YangMills and Higgs fields is larger then some critical value. This critical value is estimated.

Note on Matrix Model with Massless Flavors ; In this note, following the work of Seiberg in hepth0211234 for the conjecture between the field theory and matrix model in the case with massive fundamental flavors, we generalize it to the case with massless fundamental flavors. We show that with a little modifications, the analysis given by Seiberg can be used directly to the case of massless flavors. Furthermore, this new method explains the insertion of delta functions in the matrix model given by Demasure and Janik in hepth0211082.

Cosmological solutions of braneworlds with warped and compact dimensions ; We study cosmological aspects of braneworld models with a warped dimension and an arbitrary number of compact dimensions. With a stabilized radion, a number of different cosmological bulk solutions are found in a general case. Both one and two brane models are considered. The Friedmann equation is calculated in each case. Particular attention is paid to six dimensional models where we find that the usual Friedmann equation can typically be recovered without finetuning.

Comments on N4 Superconformal Extension of the Calogero Model ; Recently it was conjectured by Gibbons and Townsend that the large n limit of an N4 superconformal extension of the nparticle Calogero model might provide a microscopic description of the extreme ReissnerNordstrom black hole near the horizon. In this paper a possibility to construct an SU1,12 invariant extension of the Calogero model is considered. We treat in detail the twoparticle case and comment on some peculiarities intrinsic to n2 generalizations.

FiveDimensional Gauge Theories and Quantum Mechanical Matrix Models ; We show how the DijkgraafVafa matrix model proposal can be extended to describe fivedimensional gauge theories compactified on a circle to four dimensions. This involves solving a certain quantum mechanical matrix model. We do this for the lift of the N1 theory to five dimensions. We show that the resulting expression for the superpotential in the confining vacuum is identical with the elliptic superpotential approach based on Nekrasov's fivedimensional generalization of SeibergWitten theory involving the relativistic elliptic CalogeroMoser, or RuijsenaarsSchneider, integrable system.

Fused integrable lattice models with quantum impurities and open boundaries ; The alternating integrable spin chain and the RSOSq1,q2;p model in the presence of a quantum impurity are investigated. The boundary free energy due to the impurity is derived, the ratios of the corresponding g functions at low and high temperature are specified and their relevance to boundary flows in unitary minimal and generalized coset models is discussed. Finally, the alternating spin chain with diagonal and nondiagonal integrable boundaries is studied, and the corresponding boundary free energy and g functions are derived.

Superconformal boundary conditions for the WZW model ; We review the most general, local, superconformal boundary conditions for the twodimensional N1 and N2 nonlinear sigma models, and analyse them for the N1 and N2 supersymmetric WZW models. We find that the gluing map between the left and right affine currents is generalised in a very specific way as compared to the constant Lie algebra automorphisms that are known.

Center of quantum group in roots of unity and the restriction of integrable models ; We show the connection between the extended center of the quantum group in roots of unity and the restriction of the XXZ model. We also give explicit expressions for operators that respect the restriction and act on the state space of the restricted models. The formulas for these operators are verified by explicit calculation for thirddegree roots; they are conjectured to hold in the general case.

On the vacua in the massless Thirring model ; We calculate the most general effective potential for the massless Thirring model in dependence of the local fields of all fermionantifermion collective excitations. We analyse the minima of this potential describing different vacua of the quantum system. We confirm the existence of the absolute minimum found in EPJC 20, 723 2001 corresponding to the chirally broken phase of the massless Thirring model. As has been shown in EPJC 20, 723 2001 this minimum is stable under quantum fluctuations.

Phantom cosmologies ; We discuss a class of phantom p varrho cosmological models. Except for phantom we admit various forms of standard types of matter and discuss the problem of singularities for these cosmologies. The singularities are different from those of standard matter cosmology since they appear for infinite values of the scale factor. We also find an interesting relation between the phantom models and standard matter models which is like the duality symmetry of string cosmology.

Symplectic structure for elastic and chiral conducting cosmic string models ; This article is based on the covariant canonical formalism and corresponding symplectic structure on phase space developed by Witten, Zuckerman and others in the context of field theory. After recalling the basic principles of this procedure, we construct the conserved bilinear symplectic current for generic elastic string models. These models describe current carrying cosmic strings evolving in an arbitrary curved background spacetime. Particular attention is paid to the special case of the chiral string for which the worldsheet current is null. Different formulations of the chiral string action are discussed in detail, and as a result the integrability property of the chiral string is clarified.

New soluble nonlinear models for scalar fields ; We extend a deformation prescription recently introduced and present some new soluble nonlinear problems for kinks and lumps. In particular, we show how to generate models which present the basic ingredients needed to give rise to dimension bubbles, having different macroscopic space dimensions on the interior and the exterior of the bubble surface. Also, we show how to deform a model possessing lumplike solutions, relevant to the discussion of tachyonic excitations, to get a new one having topological solutions.

Supersymmetric intersecting D6branes and chiral models on the T6Z4 x Z2 orbifold ; Intersecting Dbrane worlds provide phenomenologically appealing constructions of four dimensional low energy string vacua. In this talk, a Z4 x Z2 orbifold background is taken into account. It is possible to obtain supersymmetric and stable chiral models. In particular, a three generation model with PatiSalam gauge group and no exotic chiral matter is presented.

On the Geometry of Coset Models with Flux ; We study the 3form flux Hmnl associated with the semiclassical geometry of GH gauged WZW models. We derive a simple, general expression for the flux in an orthonormal frame and use it to explicitly verify conformal invariance to the leading order in a'. For supersymmetric models, we briefly revisit the conditions for enhanced supersymmetry. We also discuss some examples of nonabelian cosets with flux.

On the Real Spectra of Calogero Model with Complex Coupling ; We study the eigenvalue problem of the rational Calogero model with the coupling of the inversesquare interaction as a complex number. We show that although this model is manifestly noninvariant under the combined parity and timereversal symmetry calPT, the eigenstates corresponding to the zero value of the generalized angular momentum have real energies.

3D Lorentzian Quantum Gravity from the asymmetric ABAB matrix model ; The asymmetric ABABmatrix model describes the transfer matrix of threedimensional Lorentzian quantum gravity. We study perturbatively the scaling of the ABABmatrix model in the neighbourhood of its symmetric solution and deduce the associated renormalization of threedimensional Lorentzian quantum gravity.

Embedding Commutative and Noncommutative Theories in the Symplectic Framework ; This paper is devoted to study gauge embedding of either commutative and noncommutative theories in the framework of the symplectic formalism. We illustrate our ideas in the Proca model, the irrotational fluid model and the noncommutative selfdual model. In the process of this new path of embedding, the infinitesimal gauge generators of the gauge embedded theory are easily and directly chosen. Among other advantages, this enables a greater control over the final Lagrangian and puts some light on the so called ''arbitrariness problem.

Deformations of WZW models ; Currentcurrent deformations for WZW models of semisimple compact groups are discussed in a sigma model approach. We start with the abelian rank one group U1. Afterwards, we keep the rank one but allow for non abelian structures by considering SU2. Finally, we present the general case of rank larger than one.

Boundary RG Flows of N2 Minimal Models ; We study boundary renormalization group flows of N2 minimal models using LandauGinzburg description of Btype. A simple algebraic relation of matrices is relevant. We determine the pattern of the flows and identify the operators that generate them. As an application, we show that the charge lattice of Bbranes in the level k minimal model is Zk2. We also reproduce the fact that the charge lattice for the Abranes is Zk1, applying the Bbrane analysis on the mirror LG orbifold.

Chiral Supersymmetric Gepner Model Orientifolds ; We explicitly construct Atype orientifolds of supersymmetric Gepner models. In order to reduce the tadpole cancellation conditions to a treatable number we explicitly work out the generic form of the oneloop Klein bottle, annulus and Moebius strip amplitudes for simple current extensions of Gepner models. Equipped with these formulas, we discuss two examples in detail to provide evidence that in this setting certain features of the MSSM like unitary gauge groups with large enough rank, chirality and family replication can be achieved.

Symplectic sigma models in superspace ; We discuss a special symplectic'' class of N 4 supersymmetric sigma models in 01 dimension with 5r bosonic and 4r complex fermionic degrees of freedom. These models can be described off shell by N 2 superfields so that only half of supersymmetries are manifest and also by N 4 superfields in the framework of the harmonic superspace approach. Using the latter, we derive the general form of the relevant bosonic target metric.

New results for deformed defects ; We extend a deformation prescription recently introduced and present some new soluble nonlinear problems for kinks and lumps. In particular, we show how to generate models which present the basic ingredients needed to give rise to dimension bubbles. Also, we show how to deform models which possess lumplike solutions, to get to new models that support kinklike solutions.

Dimensional Reduction of Nonlinear Gauge Theories ; We investigate an extension of 2D nonlinear gauge theory from the Poisson sigma model based on Lie algebroid to a model with additional twoform gauge fields. Dimensional reduction of 3D nonlinear gauge theory yields an example of such a model, which provides a realization of Courant algebroid by 2D nonlinear gauge theory. We see that the reduction of the base structure generically results in a modification of the target algebroid structure.

Gravity localisation in a 6dimensional brane world ; We study a 6dimensional EinsteinBornInfeldHiggs model. In the limit of infinite BornInfeld coupling, this model reduces to an EinsteinAbelianHiggs model, in which gravity localising solutions were shown to exist. In this proceeding, we discuss further properties of the gravity localising solutions as well as of the solutions in the limit of vanishing cosmological constant.

Duality in Fuzzy Sigma Models ; Nonlinear sigma' models in two dimensions have BPS solitons which are solutions of self and antiselfduality constraints. In this paper, we find their analogues for fuzzy sigma models on fuzzy spheres which were treated in detail by us in earlier work. We show that fuzzy BPS solitons are quantized versions of Bott projectors', and construct them explicitly. Their supersymmetric versions follow from the work of S. Kurkcuoglu.

Localized gravity in noncompact superstring models ; We discuss a stringtheoryderived mechanism for localized gravity, which produces a deviation from Newton's law of gravitation at cosmological distances. This mechanism can be realized for general noncompact CalabiYau manifolds, orbifolds and orientifolds. After discussing the crossover scale and the thickness in these models we show that the localized higher derivative terms can be safely neglected at observable distances. We conclude by some observations on the massless open string spectrum for the orientifold models.

Exact solution of the A1n1 trigonometric vertex model with nondiagonal open boundaries ; The A1n1 trigonometric vertex model with it generic nondiagonal boundaries is studied. The doublerow transfer matrix of the model is diagonalized by algebraic Bethe ansatz method in terms of the intertwiner and the corresponding facevertex relation. The eigenvalues and the corresponding Bethe ansatz equations are obtained.

The ThirringWess Model Revisited A Functional Integral Approach ; We consider the WessZuminoWitten theory to obtain the functional integral bosonization of the ThirringWess model with an arbitrary regularization parameter. Proceeding a systematic of decomposing the Bose field algebra into gaugeinvariant and gaugenoninvariant field subalgebras, we obtain the local decoupled quantum action. The generalized operator solutions for the equations of motion are reconstructed from the functional integral formalism. The isomorphism between the QED2 QCD2 with broken gauge symmetry by a regularization prescription and the Abelian nonAbelian ThirringWess model with a fixed bare mass for the meson field is established.

Determinant Formulas for Matrix Model Free Energy ; The paper contains a new nonperturbative representation for subleading contribution to the free energy of multicut solution for hermitian matrix model. This representation is a generalisation of the formula, proposed by Klemm, Marino and Theisen for two cut solution, which was obtained by comparing the cubic matrix model with the topological Bmodel on the local CalabiYau geometry hat II and was checked perturbatively. In this paper we give a direct proof of their formula and generalise it to the general multicut solution.

N4 supersymmetric EguchiHanson sigma model in d1 ; We show that it is possible to construct a supersymmetric mechanics with four supercharges possessing not conformally flat target space. A general idea of constructing such models is presented. A particular case with EguchiHanson target space is investigated in details we present the standard and quotient approaches to get the EguchiHanson model, demonstrate their equivalence, give a full set of nonlinear constraints, study their properties and give an explicit expression for the target space metric.

The Timedependent Supersymmetric Configurations in Mtheory and Matrix Models ; In this paper, we study the halfsupersymmetric timedependent configurations in Mtheory and their matrix models. We find a large class of 11D supergravity solutions, which keeps sixteen supersymmetries. Furthermore, we investigate the isometries of these configurations and show that in general these configurations have no supernumerary supersymmetries. And also we define the Matrix models in these backgrounds following Discrete LightCone Quantization DLCQ prescription.

Bethe Ansatz for a Quantum Supercoset Sigma Model ; We study an integrable conformal OSp2m 22m supercoset model as an analog to the AdS5 X S5 superstring worldsheet theory. Using the known Smatrix for this system, we obtain integral equations for states of large particle density in an SU2 sector, which are exact in the sigma model coupling constant. As a check, we derive as a limit the general classical Bethe equation of Kazakov, Marshakov, Minahan, and Zarembo. There are two distinct quantum expansions around the wellstudied classical limit, the lambda12 effects and the 1J effects. Our approach captures the first type, but not the second.

NonAbelian Brane Worlds The Open String Story ; We extend the string model building rules for the construction of chiral supersymmetric Type I compactifications on smooth CalabiYau manifolds. These models contain stacks of D9branes endowed with general stable Un bundles on their worldvolume and D5branes wrapping holomorphic curves on the CalabiYau.

CalabiYau Manifolds and the Standard Model ; For any subgroup G of On, define a Gmanifold to be an ndimensional Riemannian manifold whose holonomy group is contained in G. Then a Gmanifold where G is the Standard Model gauge group is precisely a CalabiYau manifold of 10 real dimensions whose tangent spaces split into orthogonal 4 and 6dimensional subspaces, each preserved by the complex structure and parallel transport. In particular, the product of CalabiYau manifolds of dimensions 4 and 6 gives such a Gmanifold. Moreover, any such Gmanifold is naturally a spin manifold, and Dirac spinors on this manifold transform in the representation of G corresponding to one generation of Standard Model fermions and their antiparticles.

More on ghosts in DGP model ; It is shown by an explicit calculation that the excitations about the selfaccelerating cosmological solution of the DvaliGabadazePorrati model contain a ghost mode. This raises serious doubts about viability of this solution. Our analysis reveals the similarity between the quadratic theory for the perturbations around the selfaccelerating Universe and an Abelian gauge model with two Stueckelberg fields.

Dilatons in curved backgrounds by the PoissonLie transformation ; Transformations between group coordinates of threedimensional conformal sigma models in the flat background and their flat, i.e. Riemannian coordinates enable to find general dilaton fields for threedimensional flat sigma models. By the PoissonLie transformation we can get dilatons for the dual sigma models in a curved background. Unfortunately, in some cases the dilatons depend on inadmissible auxiliary variables so the procedure is not universal. The cases where the procedure gives proper and nontrivial dilatons in curved backgrounds are investigated and results given.

Conserved Charges in the Principal Chiral Model on a Supergroup ; The classical principal chiral model in 11 dimensions with target space a compact Lie supergroup is investigated. It is shown how to construct a local conserved charge given an invariant tensor of the Lie superalgebra. We calculate the superPoisson brackets of these currents and argue that they are finitely generated. We show how to derive an infinite number of local charges in involution. We demonstrate that these charges Poisson commute with the nonlocal charges of the model.

Thermal flow in the gravitational On model ; We study the massless flow from the critical point dilute loops to the lowtemperature phase dense loops of the On loop gas model when the model is coupled to 2D gravity. The flow is generated by the gravitationally dressed thermal operator Phi1,3 coupled to the renormalized loop tension lambda TTc. We find that the susceptibility as a function of the thermal coupling lambda and the cosmological constant mu satisfies a simple transcendental equation.

Topological twisted sigma model with Hflux revisited ; In this paper we revisit the topological twisted sigma model with Hflux. We explicitly expand and then twist the worldsheet Lagrangian for biHermitian geometry. we show that the resulting action consists of a BRST exact term and pullback terms, which only depend on one of the two generalized complex structures and the Bfield. We then discuss the topological feature of the model.

The oneloop renormalization of the gauge sector in the noncommutative standard model ; In this paper we construct a version of the standard model gauge sector on noncommutative spacetime which is oneloop renormalizable to first order in the expansion in the noncommutativity parameter theta. The oneloop renormalizability is obtained by the SeibergWitten redefinition of the noncommutative gauge potential for the model containing the usual six representations of matter fields of the first generation.

Lax pair and Darboux transformation of noncommutative UN principal chiral model ; We present a noncommutative generalization of Lax formalism of UN principal chiral model in terms of a oneparameter family of flat connections. The Lax formalism is further used to derive a set of parametric noncommutative Backlund transformation and an infinite set of conserved quantities. From the Lax pair, we derive a noncommutative version of the Darboux transformation of the model.

High spin particles with spinmass coupling II ; The classical and quantum model of high spin particles with spinmass coupling is presented in this paper. The mass spectrum of the model is symmetric with respect to particleantiparticle exchange. The quantum model contains elementary particles and the cluster states generating infinite degeneracy of the mass spectrum.

On the SU21 WZW model and its statistical mechanics applications ; Motivated by a careful analysis of the Laplacian on the supergroup SU21 we formulate a proposal for the state space of the SU21 WZNW model. We then use properties of hatsl21 characters to compute the partition function of the theory. In the special case of level k1 the latter is found to agree with the properly regularized partition function for the continuum limit of the integrable sl21 3bar3 superspin chain. Some general conclusions applicable to other WZNW models in particular the case k12 are also drawn.

Nonadiabatic quantum effects from a Standard Model timedependent Higgs vev ; We consider the timedependence of the Higgs vacuum expectation value vev given by the dynamics of the Standard Model and study the nonadiabatic production of both bosons and fermions, which is intrinsically nonperturbative. In the Hartree approximation, we analyse the general expressions that describe the dissipative dynamics due to the backreaction of the produced particles. In particular, we solve numerically some relevant cases for the Standard Model phenomenology in the regime of relatively small oscillations of the Higgs vev.

Topological DBranes and Commutative Algebra ; We show that questions concerning the topological Bmodel on a CalabiYau manifold in the LandauGinzburg phase can be rephrased in the language of commutative algebra. This yields interesting and very practical methods for analyzing the model. We demonstrate how the relevant Ext groups and superpotentials can be computed efficiently by computer algebra packages such as Macaulay. This picture leads us to conjecture a general description of Dbranes in linear sigma models in terms of triangulated categories. Each phase of the linear sigma model is associated with a different presentation of the category of Dbranes.

The universality spectrum of stable unsuperstable theories ; It is shown that if T is stable unsuperstable, and aleph1 lambda cflambda 2aleph0, or 2aleph0 mu lambda cflambda mualeph0 then T has no universal model in cardinality lambda, and if e.g. alephomega 2aleph0 then T has no universal model in alephomega. These results are generalized to kappa cfkappa kappa T in the place of aleph0. Also if there is a universal model in lambda T, T stable and kappa kappa T then there is a universal tree of height kappa 1 in cardinality lambda .

On a Spector ultrapower of the Solovay model ; We prove that a Spectorlike ultrapower extension gN of a countable Solovay model gM where all sets of reals are Lebesgue measurable is equal to the set of all sets constructible from reals in a generic extension gMal where al is a random real over gM. The proof involves an almost everywhere uniformization theorem in the Solovay model.

mstructures determine integral homotopy type ; This paper proves that the functor C that sends pointed, simplyconnected CWcomplexes to their chaincomplexes equipped with diagonals and iterated higher diagonals, determines their integral homotopy type even inducing an equivalence of categories between the category of CWcomplexes up to homotopy equivalence and a certain category of chaincomplexes equipped with higher diagonals. Consequently, C is an algebraic model for integral homotopy types similar to Quillen's model of rational homotopy types. For finite CW complexes, our model is finitely generated. Our result implies that the geometrically induced diagonal map with all higher diagonal'' maps like those used to define Steenrod operations collectively determine integral homotopy type.

Large deviations and queueing networks methods for rate function identification ; This paper considers the problem of rate function identification for multidimensional queueing models with feedback. A set of techniques are introduced which allow this identification when the model possesses certain structural properties. The main tools used are representation formulas for exponential integrals, weak convergence methods, and the regularity properties of associated Skorokhod Problems. Two examples are treated as special cases of the general theory the classical Jackson network and a model for processor sharing.

Maximally symmetric trees ; We characterize the best'' model geometries for the class of virtually free groups, and we show that there is a countable infinity of distinct best'' model geometries in an appropriate sensethese are the maximally symmetric trees. The first theorem gives several equivalent conditions on a bounded valence, cocompact tree T without valence 1 vertices saying that T is maximally symmetric. The second theorem gives general constructions for maximally symmetric trees, showing for instance that every virtually free group has a maximally symmetric tree for a model geometry.

Limit theorems for the painting of graphs by clusters ; We consider a generalization of the socalled divide and color model recently introduced by Haggstrom. We investigate the behaviour of the magnetization in large boxes and its fluctuations. Thus, laws of large numbers and Central Limit theorems are proved, both quenched and annealed. We show that the properties of the underlying percolation process roughly influence the behaviour of the colorying model. In the subcritical case, the limit magnetization is deterministic and the Central Limit Theorem admits a Gaussian limit. A contrario, the limit magnetization is not deterministic in the supercritical case and the limit of the Central Limit Theorem is not Gaussian, except in the particular model with exactly two colors which are equally probable.

A paradox of diffusion market model related with existence of winning combinations of options ; We consider strategies of investments into options and diffusion market model. It is shown that there exists a correct proportion between put and call in the portfolio such that the average gain is almost always positive for a generic Black and Scholes model. This gain is zero if and only if the market price of risk is zero. It is discussed a paradox related to the corresponding loss of option's seller.

Applications of PerronFrobenius Theory to Population Dynamics ; By the use of PerronFrobenius theory, simple proofs are given of the Fundamental Theorem of Demography and of a theorem of Cushing and Yicang on the net reproductive rate occurring in matrix models of population dynamics. The latter result is further refined with some additional nonnegative matrix theory. When the fertility matrix is scaled by the net reproductive rate, the growth rate of the model is 1. More generally, we show how to achieve a given growth rate for the model by scaling the fertility matrix. Demographic interpretations of the results are given.

On Z2twisted representation of vertex operator superalgebras and the Ising model SVOA ; We investigate a general theory of the Z2twisted representations of vertex operator superalgebras. Certain onetoone correspondence theorems are established. We also give an explicit realization of the Ising model SVOA and its Z2twisted modules. As an application, we obtain the Gerald Hoehn's Babymonster SVOA VB and its Z2twisted module VBtw from the moonshine VOA Vnat by cutting off the Ising models. It is also shown in this paper that Aut VB is finite.

A Carleson type theorem for a Cantor group model of the scattering transform ; We consider a basic dadic model for the scattering transform on the line. We prove L2 bounds for this scattering transform and a weak L2 bound for a Carleson type maximal operator. The latter implies boundedness of dadic models of generalized eigenfunctions of Dirac type operators with potential in L2R. We show that this result cannot be obtained by estimating the terms in the natural multilinear expansion of the scattering transform.

The degree distribution in bipartite planar maps applications to the Ising model ; We characterize the generating function of bipartite planar maps counted according to the degree distribution of their black and white vertices. This result is applied to the solution of the hard particle and Ising models on random planar lattices. We thus recover and extend some results previously obtained by means of matrix integrals. Proofs are purely combinatorial and rely on the idea that planar maps are conjugacy classes of trees. In particular, these trees explain why the solutions of the Ising and hard particle models on maps of bounded degree are always algebraic.

Discrete Approximation of NonCompact Operators Describing ContinuumofAlleles Models ; We consider the eigenvalue equation for the largest eigenvalue of certain kinds of noncompact linear operators given as the sum of a multiplication and a kernel operator. It is shown that, under moderate conditions, such operators can be approximated arbitrarily well by operators of finite rank, which constitutes a discretization procedure. For this purpose, two standard methods of approximation theory, the Nystrom and the Galerkin method, are generalized. The operators considered describe models for mutation and selection of an infinitely large population of individuals that are labeled by real numbers, commonly called continuumofalleles COA models.

On Bethe vectors in the XXZ model at roots of unity ; We give a construction of creation operators responsible for appearance of Bethe vectors with the same eigenvalues of the transfermatrix for the inhomogeneous arbitrary spin XXZ model at roots of unity with particular quasiperiodic boundary conditions. This construction generalizes the similar one, recently obtained by K.Fabricius and B.M.McCoy, for the homogeneous sixvertex model with periodic boundary conditions. Even in the last case, the given proof for the main formulae are simpler than the original one.

The parabolic Anderson model ; This is a survey on the intermittent behavior of the parabolic Anderson model, which is the Cauchy problem for the heat equation with random potential on the lattice Zd. We first introduce the model and give heuristic explanations of the longtime behavior of the solution, both in the annealed and the quenched setting for timeindependent potentials. We thereby consider examples of potentials studied in the literature. In the particularly important case of an i.i.d. potential with doubleexponential tails we formulate the asymptotic results in detail. Furthermore, we explain that, under mild regularity assumptions, there are only four different universality classes of asymptotic behaviors. Finally, we study the moment Lyapunov exponents for spacetime homogeneous catalytic potentials generated by a Poisson field of random walks.

A new model for the theta divisor of the cubic threefold ; In this paper we give a birational model for the theta divisor of the intermediate Jacobian of a generic cubic threefold X. We use the standard realization of X as a conic bundle and a 4dimensional family of plane quartics which are totally tangent to the discriminant quintic curve of such a conic bundle structure. The additional data of an even theta characteristic on the curves in the family gives us a model for the theta divisor.