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Semirelativistic potential model for lowlying threegluon glueballs ; The threegluon glueball states are studied with the generalization of a semirelativistic potential model giving good results for twogluon glueballs. The Hamiltonian depends only on 3 parameters fixed on twogluon glueball spectra the strong coupling constant, the string tension, and a gluon size which removes singularities in the potential. The Casimir scaling determines the structure of the confinement. Lowlying JPC states are computed and compared with recent lattice calculations. A good agreement is found for 1 and 3 states, but our model predicts a 2 state much higher in energy than the lattice result. The 0 mass is also computed.

The controversy about 1mQ duality violation ; a quark model point of view ; A detailed discussion based on exact calculations, possible in the non relativistic quark model, is given to show that there is no 1mQ term in the heavy quark expansion of totally integrated semileptonic decay rates. More generally, it is shown that OPE holds with very few terms in the expansion, at least in the harmonic oscillator model.

The model of particle production by strong external sources ; Using some knowledge of multiplicity disributions for high energy reactions, it is possible to propose a simple analytical model of particle production by strong external sources. The model describes qualitatively most peculiar properties of the distributions. The generating function of the distribution varies so drastically as it can happen at phase transitions.

Stability of the normal vacuum in multiHiggsdoublet models ; We show that the vacuum structure of a generic multiHiggsdoublet model shares several important features with the vacuum structure of the two and three Higgsdoublet model. In particular, one can still define the usual charge breaking, spontaneous CP breaking and normal charge and CP preserving stationary points. We analyse the possibility of charge or spontaneous CP breaking, by studying the relative depth of the potential in each of the possible stationary points.

Tetrons a possible Solution to the Family Problem ; A model is presented, in which fermion and vector boson states are constructed from constituents tetrons. The model encodes all observed structures and phenomena of elementary particle physics in group theoretic items of the permutation group S4. Details of the model like symmetry breaking, distribution of charges and mass generation are worked out. As a sideproduct a deeper understanding of parity violation is obtained.

Higgs at the Tevatron in Extended Supersymmetric Models ; Supersymmetric models with an additional singlet field offer the Higgs boson the possibility to decay to two pseudoscalars, a. If the mass of these pseudoscalars is above the b bbar threshold, a b bbar is generically the dominant decay mode. The decay h a a b bbar b bbar may be seen above backgrounds at the Tevatron if the Higgs production cross section is enhanced relative to that of the standard model.

Hadronic Interactions at Cosmic Ray Energies ; General physics of very high energy hadronic interactions is discussed. Special attention is payed to the contribution of semihard processes to the interaction dynamics and to the role of parton shadowing and parton density saturation. In particular, the implementation of nonlinear interaction effects in the QGSJETII model is discussed in detail. The predictions of the model are compared to selected accelerator data, including ones of the RHIC collider, and the relation to the calculated extensive air shower characteristics is discussed. Finally, the potential of accelerator and cosmic ray experiments for constraining model predictions is analyzed.

The MSSM on the Interval ; We review electroweak symmetry breaking in supersymmetric models with a compact fifth dimension, the interval. We show how boundary conditions for hypermultiplets can be obtained dynamically by brane mass terms and present formulae for the spectrum in the presence of general bulk mass matrices. After giving a brief overview on the literature of models, we describe in detail a recently proposed model that at energies below the compactification scale reduces to the MSSM with a very peculiar superpartner spectrum.

A simple explanation of the PVLAS anomaly in spontaneously broken mirror models ; The PVLAS anomaly can be explained if there exist millicharged particles of mass stackrelsim 0.1 eV and electric charge epsilon sim 106 e. We point out that such particles occur naturally in spontaneously broken mirror models. We argue that this interpretation of the PVLAS anomaly is not in conflict with astrophysical constraints due to the self interactions of the millicharged particles which lead them to be trapped within stars. This conclusion also holds for a generic paraphoton model.

Retrofitted Gravity Mediation without the Gravitinooverproduction Problem ; We propose a retrofitted gravity mediation model which alleviates the gravitino overproduction from decays of an inflaton and a supersymmetry breaking field. In the model, we introduce an approximate U1 symmetry under which the supersymmetry breaking field is charged, although it is broken by a mass term of messenger fields to generate gaugino masses of order the weak scale. In a lowscale inflation model, we find regions in which the gravitino overproduction problem is avoided.

Excitedstate thermodynamics ; In the last several years, the Casimir energy for a variety of 11dimensional integrable models has been determined from the exact Smatrix. It is shown here how to modify the boundary conditions to project out the lowestenergy state, which enables one to find excitedstate energies. This is done by calculating thermodynamic expectation values of operators which generate discrete symmetries. This is demonstrated with a number of perturbed conformal field theories, including the Ising model, the threestate Potts model, bf Zn parafermions, Toda minimal Smatrices, and massless Goldstinos.

A Novel Chiral Boson ; We introduce a new model describing a bosonic system with chiral properties. It consists of a free boson with two peculiar couplings to the background geometry which generalizes the FeigenFuchsDotsenkoFateev construction. By choosing the two background charges of the model, it is possible to achieve any prefixed value of the left and right central charges and, in particular, obtain chiral bosonization. A supersymmetric version of the model is also given. We use the latter to identify the effective action induced by chiral superconformal matter.

OnePoint Functions of Loops and Constraints Equations of the MultiMatrix Models at finite N ; We derive onepoint functions of the loop operators of Hermitian matrixchain models at finite N in terms of differential operators acting on the partition functions. The differential operators are completely determined by recursion relations from the SchwingerDyson equations. Interesting observation is that these generating operators of the onepoint functions satisfy W1inftylike algebra. Also, we obtain constraint equations on the partition functions in terms of the differential operators. These constraint equations on the partition functions define the symmetries of the matrix models at offcritical point before taking the double scaling limit.

Unitary And Hermitian Matrices In An External Field II The Kontsevich Model And Continuum Virasoro Constraints ; We give a simple derivation of the Virasoro constraints in the Kontsevich model, first derived by Witten. We generalize the method to a model of unitary matrices, for which we find a new set of Virasoro constraints. Finally we discuss the solution for symmetric matrices in an external field.

Intersection Theory, Integrable Hierarchies and Topological Field Theory ; In these lecture notes we review the various relations between intersection theory on the moduli space of Riemann surfaces, integrable hierarchies of KdV type, matrix models, and topological quantum field theories. We explain in particular why matrix integrals of the type considered by Kontsevich naturally appear as taufunctions associated to minimal models. Our starting point is the extremely simple form of the string equation for the topological p,1 models, where the socalled BakerAkhiezer function is given by a generalized Airy function.

A New Deformation of WInfinity and Applications to the Twoloop WZNW and Conformal Affine Toda Models ; We construct a centerless Winfinity type of algebra in terms of a generator of a centerless Virasoro algebra and an abelian spin1 current. This algebra conventionally emerges in the study of pseudodifferential operators on a circle or alternatively within KP hierarchy with Watanabe's bracket. Construction used here is based on a special deformation of the algebra winfty of area preserving diffeomorphisms of a 2manifold. We show that this deformation technique applies to the twoloop WZNW and conformal affine Toda models, establishing henceforth Winfty invariance of these models.

Matrix Model Perturbed by Higher Order Curvature Terms ; The critical behaviour of the D0 matrix model with potential perturbed by nonlocal term generating touchings between random surfaces is studied. It is found that the phase diagram of the model has many features of the phase diagram of discretized Polyakov's bosonic string with higher order curvature terms included. It contains the phase of smooth Liouville surfaces, the intermediate phase and the phase of branched polymers. The perturbation becomes irrelevant at the first phase and dominates at the third one.

Running Gauge Couplings and Thresholds in the Type II Superstring ; A distinctive feature of string unification is the possibility of unification by a nonsimplylaced group. This occurs most naturally in four dimensional typeII string models where the gauge symmetry is realized by KacMoody algebras at different levels. We investigate the running coupling constants and the oneloop thresholds for such general models. As a specific case, we examine a rm SU3times U1times U1 model and find that the threshold corrections lead to a small 6 increase in the unification scale.

An Infinite Number of Commuting Quantum hatWinfty Charges in the SL2,RU1 Coset Model ; The conformal noncompact SL2,RU1 coset model in two dimensions has been recently shown to embody a nonlinear hatWinfty current algebra, consisting of currents of spin geq 2 including the energymomentum tensor. In this letter we explicitly construct an infinite set of commuting quantum hatWinfty charges in the model with k1. These commuting quantum charges generate a set of infinitely many compatible flows quantum KP flows, which maintain the nonlinear hatWinfty current algebra invariant.

BRST cohomology ring in 2D gravity coupled to minimal models ; The ring structure of LianZuckerman states for q,p minimal models coupled to gravity is shown to be cal Rcal R0otimes bf C w,w1 where cal R0 is the ring of ghost number zero operators generated by two elements and w is an operator of ghost number 1. Some examples are discussed in detail. For these models the currents are also discussed and their algebra is shown to contain the Virasoro algebra.

Deformations of Dynamics Associated to the Chiral Potts Model ; We describe deformations of nonlinear birational representations of discrete groups generated by involutions, having their origin in the theory of the symmetric fivestate Potts model. One of the deformation parameters can be seen as the number q of states of a chiral Potts models. This analogy becomes exact when q is a Fermat number. We analyze the stability of the corresponding dynamics, with a particular attention to orbits of finite order.

Modular Groups for Twisted Narain Models ; We demonstrate how to find modular discrete symmetry groups for ZN orbifolds. The Z7 orbifold is treated in detail as a nontrivial example of a 2,2 orbifold model. We give the generators of the modular group for this case which, surprisingly, does not contain sltz3 as had been speculated. The treatment models with discrete Wilson lines is also discussed. We consider examples which demonstrate that discrete Wilson lines affect the modular group in a nontrivial manner. In particular, we show that it is possible for a Wilson line to break SL2,bf Z.

Scattering States and Symmetries in the Matrix Model and Two Dimensional String Theory ; We study the correspondence between the linear matrix model and the interacting nonlinear string theory. Starting from the simple matrix harmonic oscillator states, we derive in a direct way scattering amplitudes of 2dimensional strings, exhibiting the nonlinear equation generating arbitrary Npoint tree amplitudes. An even closer connection between the matrix model and the conformal string theory is seen in studies of the symmetry algebra of the system.

RG flows and resonance scattering amplitudes ; We review recent progresses in the study of factorized resonance scattering Smatrices. The resonance amplitudes are introduced through a suitable analytical continuation of the ADE Toda Smatrices. By using the thermodynamic Bethe ansatz approach we are able to compute the ground state energy, which describes a rich pattern of flows interpolating between the central charges of the coset models based on the ADE Lie algebras. We also present the simplest resonance phi3'' scattering model and discuss its relation with new flows in nonunitary minimal models. Further generalizations are discussed in terms of certain asymptotic conditions in a family of resonance'' functional hierarchies.

Exact Duality Symmetries in CFT and String Theory ; The duality symmetries of WZW and coset models are discussed. The exact underlying symmetry responsible for semiclassical duality is identified with the symmetry under affine Weyl transformations. This identification unifies the treatement of duality symmetries and shows that in the compact and unitary case they are exact symmetries of string theory to all orders in alpha' and in the string coupling constant. Noncompact WZW models and cosets are also discussed. A toy model is analyzed suggesting that duality will not generically be a symmetry.

Braiding in Conformal Field Theory and Solvable Lattice Models ; Braiding matrices in rational conformal field theory are considered. The braiding matrices for any two block four point function are computed, in general, using the holomorphic properties of the blocks and the holomorphic properties of rational conformal field theory. The braidings of SUNk with the fundamental are evaluated and are used as examples. Solvable interaction round the face lattice models are constructed from these braiding matrices, and their Boltzmann weights are given. This allows, in particular, for the derivation of the Boltzmann weights of such solvable height models.

Quantum Group Gauge Theories and Covariant Quantum Algebras ; The algebraic formulation of the quantum group gauge models in the framework of the Rmatrix approach to the theory of quantum groups is given. We consider gauge groups taking values in the quantum groups and noncommutative gauge fields transformed as comodules under the coaction of the gauge quantum group Gq. Using this approach we construct the quantum deformations of the topological ChernSimons models, nonabelian gauge theories and the Einstein gravity. The noncommutative fields in these models generate Gqcovariant quantum algebras.

Extended NonAbelian Gauge Symmetries in Classical WZNW Model ; The present paper is revised copy of hepth9303087 in which higher spin extensions of the nonabelian gauge symmetries for the classical WZNW model are considered. Both linear and nonlinear realizations of the extended affine KacMoody algebra are obtained. A characteristic property of the WZNW model is that it admits a higher spin linear realization of the extended affine KacMoody algebra which is equivalent to the corresponding higher spin nonlinear realization of the same algebra. However, in both cases the higher spin currents do not form an invariant space with respect to their generating transformations. This makes it imposible for this symmetry to be gauged.

Naked Singularities in FourDimensional String Backgrounds ; It is shown that gauged nonlinear sigma models can be always deformed by terms proportional to the field strength of the gauge fields nonminimal gauging. These deformations can be interpreted as perturbations, by marginal operators, of conformal coset models. When applied to the SL2,RSU2U1U1 WZWN model, a large class of fourdimensional curved spacetime backgrounds are obtained. In particular, a naked singularity may form at a time when the volume of the universe is different from zero.

On the model of the relativistic particle with curvature and torsion ; Two integrals along the world trajectory of its curvature and torsion are added to the standard action for the pointlike spinless relativistic particle. Since here the threedimensional spacetime is considered at the beginning, the torsion of the world curve is defined with a sign in contrast to the previous consideration V. V. Nesterenko, J. Math. Phys. 32, 3315 1991. Upon obtaining a complete set of constraints in the phase space a generalized Hamiltonian description of a new version of the model is constructed. This enables one to quantize the model canonically and to derive exactly the relation between the spin and mass of the states.

Breakdown of Duality in 0,2 Superstring Models ; After pointing out the role of the compactification lattice for spectrum calculations in orbifold models, I discuss modular discrete symmetry groups for ZN orbifolds. I consider the Z7 orbifold as a nontrivial example of a 2,2 model and give the generators of the modular group for this case, which does not contain SL2,bf Z3 as had been speculated. I also discuss how to treat cases where quantized Wilson lines are present. I consider in detail an example, demonstrating that quantized Wilson lines affect the modular group in a nontrivial manner. In particular, I show that it is possible for a Wilson line to break SL2,bf Z.

Conformal nonAbelian Thirring models ; The LiePoisson structure of nonAbelian Thirring models is discussed and the Hamiltonian quantization of these theories is carried out. The consistency of the Hamiltonian quantization with the path integral method is established. It is shown that the space of nonAbelian Thirring models contains the nonperturbative conformal points which are in onetoone correspondence with general solutions of the Virasoro master equation. A BRST nature of the mastert equation is clarified.

Topological current algebras in two dimensions ; Twodimensional topological field theories possessing a nonabelian current symmetry are constructed. The topological conformal algebra of these models is analysed. It differs from the one obtained by twisting the N2 superconformal models and contains generators of dimensions 1, 2 and 3 that close a linear algebra. Our construction can be carried out with one and two bosonic currents and the resulting theories can be interpreted as topological sigma models for group manifolds

More Gravitational Anyons ; The anyonic behaviour of massive spinning point particles coupled to linearized massive vector ChernSimons gravity is studied. This model constitutes the uniform spin2 generalization of the vector model formed by coupling charged point particles to the topological massive MaxwellCS action. It turns out that, for this model, the linearized first order triadic ChernSimons term is the source of the anyonic behaviour we found. This is in constrast with the third order topologically massive gravity, where the anyonic behaviour does not stem in its thirdorder LorentzChernSimons term, the second order Einstein's action .

The SineGordon Solitons as a NBody Problem ; We consider the Nsoliton solutions in the sineGordon model as a Nbody problem. This leads to a relativistic generalization of the Calogero model first introduced by Ruijsenaars. We show that the fundamental Poisson bracket of the Lax matrix is quadratic, and the rmatrix is a dynamical one. This is in contrast to the Calogero model where the fundamental Poisson bracket of the Lax matrix is linear.

The Exact Tachyon BetaFunction for the WessZuminoWitten Model ; We derive an exact expression for the tachyon betafunction for the WessZuminoWitten model. We check our result up to three loops by calculating the threeloop tachyon betafunction for a general nonlinear sigmamodel with torsion, and then specialising to the case of the WZW model.

Can gravity make the Higgs particle light ; The spontaneous symmetry breaking theory of gravity is examined, assuming that the vacuum expectation value of the standard model Higgs is also responsible for the generation of the Planck mass. In this model the physical Higgs couples only with gravitational strength to matter. At presently accessible energies the theory is indistinguishable from the standard model without Higgs boson and is in agreement with all existing data.At energies above the Fermi scale new dynamics should occur.

Algebraic Aspects of BetheAnsatz ; In these lectures the introduction to algebraic aspects of Bethe Ansatz is given. The applications to the seminal spin 12 XXX model is discussed in detail and the generalization to higher spin as well as XXZ and lattice SineGordon model are indicated. The origin of quantum groups and their appearance in CFT models is explained. The text can be considered as a guide to the research papers in this field.

QCD on a Tree ; A model is proposed which can be regarded as a mean field approximation for pure lattice QCD and chiral field. It always possesses a phase transition between a strong coupling phase where it reduces to a oneplaquette integral and a nontrivial weak coupling one. For the UN gauge group, it is equivalent to some multimatrix model. This analogy allows for determining possible large N critical regimes thus generalizing the GrossWitten phase transition in the oneplaquetee model.

Twomatrix model and c1 string theory ; We show that the most general twomatrix model with bilinear coupling underlies c1 string theory. More precisely we prove that W1infty constraints, a subset of the correlation functions and the integrable hierarchy characterizing such twomatrix model, correspond exactly to the W1infty constraints, to the discrete tachyon correlation functions and to the integrable hierarchy of the c1 string.

Massive p,qsupersymmetric sigma models revisited ; We recently obtained the conditions on the couplings of the general twodimensional massive sigmamodel required by p,qsupersymmetry. Here we compute the Poisson bracket algebra of the supersymmetry and central Noether charges, and show that the action is invariant under the automorphism group of this algebra. Surprisingly, for the 4,4 case the automorphism group is always a subgroup of SO3, rather than SO4. We also reanalyse the conditions for the 2,2 and 4,4 supersymmetry of the zero torsion models without assumptions about the central charge matrix.

AGenus and the Sigma Model ; This set of lecture notes presents a pedantic derivation of the connection between the hat A genus of spacetime's loop space and the genus one partition function of the N12 sigma model. It concludes with some remarks on possible generalizations of the hat A genus which follow naturally from the stringy' pointofview but have yet to be explored mathematically. This set of lecture notes is geared towards a mathematical audience unfamiliar with the N12 sigma model.

Sectors of Mutually Local Fields in Integrable Models of Quantum Field Theory ; It is known that 2D field theories admit several sectors of mutually local fields so as two fields from different sectors are mutually nonlocal. We show that any onepartical integrable model with bf Z2 symmetry contains three sectors bosonic, fermionic and disorder' one. We generalize the form factor axioms to fermionic and disorder' sectors. For the particular case of the sinhGordon model we obtain several form factors in these sectors.

The Field Theory Limit of Integrable Lattice Models ; The lightcone approach is reviewed. This method allows to find the underlying quantum field theory for any integrable lattice model in its gapless regime. The relativistic spectrum and Smatrix follows straightforwardly in this way through the Bethe Ansatz. We show here how to derive the infinite number of local commuting and nonlocal and noncommuting conserved charges in integrable QFT, taking the massive Thirring model sineGordon as an example. They are generated by quantum monodromy operators and provide a representation of qdeformed affine Lie algebras UqhatG. Based on lectures delivered at the XXXq Karpacz Winter School, Poland, February 1426, 1994.

Nambu mass hierarchies in low energy string models ; This paper explores a recent idea of Nambu to generate hierarchies among Yukawa couplings in the context of effective supergravity and superstrings models. The Yukawa couplings are homogeneous functions of the moduli and a geometrical constraint between them with a crucial role in the Nambu mechanism is found in a class of models of noscale type. The Yukawas are dynamical variables at low energy to be determined by a minimization process. Based on the talk given at ICHEP94, Glasgow, july 1994

Quantum Gravity via Random Triangulations of R4 and Gravitons as Goldstone Bosons of SL4O4 ; A model of random triangulations of a domain in R4 is presented. The global symmetries of the model include SL4 transformations and translations. If a stable microscopic scale exists for some range of parameters, the model should be in a translation invariant phase where SL4 is spontaneously broken to O4. In that phase, SL4 Ward identities imply that the correlation length in the spin two channel of a symmetric tensor field is infinite. Consequently, it may be possible to identify the continuum limit of four dimensional Quantum Gravity with points inside that phase.

Higher Derivative FourFermion Model in Curved Spacetime ; We discuss the phase structure of a higher derivative fourfermion model in four dimensions in curved spacetime in frames of the frac1Ncexpansion. First, we evaluate in our model the effective potential of two composite scalars in the linear curvature approximation using a local momentum representation in curved spacetime for the higherderivative propagator which naturally appears. The symmetry breaking phenomenon and phase transition induced by curvature are numerically investigated. A numerical study of the dynamically generated fermionic mass, which depends on the coupling constants and on the curvature, is also presented.

On Conformal Properties of the Dualized SigmaModels ; We have calculated the firstorder betafunctions for a sigmamodel with dilaton dualized with respect to an arbitrary Lie group that acts without isotropy. We find that nonabelian duality preserves conformal invariance for semisimple groups, but in general there is an extra contribution to the betafunction proportional to the trace of the structure constants, which cannot be absorbed into an additional dilaton shift. Two particular examples, a Bianchi V cosmological background and the G otimes G WZW model, are discussed.

Topological Strings from WZW Models ; We show that the BRST structure of the topological string is encoded in the small'' N4 superconformal algebra, enabling us to obtain, in a nontrivial way, the string theory from hamiltonian reduction of A11. This leads to the important conclusion that not only ordinary string theories, but topological strings as well, can be obtained, or even defined, by hamiltonian reduction from WZW models. Using two different gradations, we find either the standard N2 minimal models coupled to topological gravity, or an embedding of the bosonic string into the topological string. We also comment briefly on the generalization to super Lie algebras Ann.

BRST quantization of gauge theories like SL2,R on inner product spaces ; Some general formulas are derived for the solutions of a BRST quantization on inner product spaces of finite dimensional bosonic gauge theories invariant under arbitrary Lie groups. A detailed analysis is then performed of SL2,R invariant models and some possible geometries of the Lagrange multipliers are derived together with explicit results for a class of SL2,R models. Gauge models invariant under a nonunimodular gauge group are also studied in some detail.

Further solutions of critical ABF RSOS models ; The restricted SOS model of Andrews, Baxter and Forrester has been studied. The finite size corrections to the eigenvalue spectra of the transfer matrix of the model with a more general crossing parameter have been calculated. Therefore the conformal weights and the central charges of the nonunitary or unitary minimal conformal field have been extracted from the finite size corrections.

On Black Holes in the Theory of Dilatonic Gravity Coupled to a Scalar Field ; Taking advantage of the representation of dilatonic gravity with the R2term under the form of lowderivative dilatonic gravity coupled to an additional scalar, we construct a general renormalizable model motivated by this theory. Exact black hole solutions are found for some special versions of the model, and their thermodynamical properties are described in detail. In particular, their horizons and temperatures are calculated. Finally, the corresponding oneloop effective action is obtained in the conformal gauge, and a number of its properties including the construction of oneloop finite modelsare briefly described.

On the U1Problem of QED2 ; QED2 with mass and flavor has in common many features with QCD, and thus is an interesting toy model relevant for four dimensional physics. The model is constructed using Euclidean path integrals and mass perturbation series. The vacuum functional is carefully decomposed into clustering states being the analogue of the thetavacuum of QCD. Finally the clustering theory can be mapped onto a generalized SineGordon model. Having at hand this bosonized version, several lessons on the thetavacuum, the U1problem and WittenVenezianotype formulas will be drawn. This sheds light on the corresponding structures of QCD.

Classical Symmetries of Some TwoDimensional Models Coupled to Gravity ; This paper is a sequel to one in which we examined the affine symmetry algebras of arbitrary classical principal chiral models and symmetric space models in two dimensions. It examines the extension of those results in the presence of gravity. The main result is that even though the symmetry transformations of the fields depend on the gravitational background, the symmetry algebras of these classical theories are completely unchanged by the presence of arbitrary gravitational backgrounds. On the other hand, we are unable to generalize the Virasoro symmetries of the flatspace theories to theories with gravity.

Folding transitions of the triangular lattice with defects ; A recently introduced model describing the folding of the triangular lattice is generalized allowing for defects in the lattice and written as an Ising model with nearestneighbor and plaquette interactions on the honeycomb lattice. Its phase diagram is determined in the hexagon approximation of the cluster variation method and the crossover from the pure Ising to the pure folding model is investigated, obtaining a quite rich structure with several multicritical points. Our results are in very good agreement with the available exact ones and extend a previous transfer matrix study.

From Principal Chiral Model to Selfdual Gravity ; It is demonstrated that the action of SUN principal chiral model leads in the limit N to infty to the action for Husain's heavenly equation. The principal chiral model in the Hilbert space L2Re1 is considered and it is shown, that in this case the chiral equation is equivalent to the Moyal deformation of Husain's heavenly equation. New method of searching for solutions to this latter equation, via Lie algebra representations in L2Re1 is given.

Two Loop Renormalization of Massive p,q Supersymmetric Sigma Models ; We calculate the betafunctions of the general massive p,q supersymmetric sigma model to two loop order using 1,0 superfields. The conditions for finiteness are discussed in relation to p,q supersymmetry. We also calculate the effective potential using component fields to one loop order and consider the possibility of perturbative breaking of supersymmetry. The effect of one loop finite local counter terms and the ultraviolet behaviour of the offshell p,q models to all orders in perturbation theory are also addressed.

On the Walgebra in the CalegeroSutherland model using the Exchange operators ; We study the Winfty algebra in the CalegeroSutherland model using the exchange operators. The presence of all the subalgebras of Winfty is shown in this model. A simplified proof for this algebra, in the symmetric ordered basics, is given. It is pointed out that the algebra contains in general, nonlinear terms. Possible connection to the nonlinear Winfty is discussed.

Logarithmic Operators and Hidden Continuous Symmetry in Critical Disordered Models ; We study the model of 2 1dimensional relativistic fermions in a random nonAbelian gauge potential at criticality. The exact solution shows that the operator expansion contains a conserved current a generator of a continuous symmetry. The presence of this operator changes the operator product expansion and gives rise to logarithmic contributions to the correlation functions at the critical point. We calculate the distribution function of the local density of states in this model and find that it follows the famous lognormal law.

Infrared Behaviour of Massless Integrable Flows entering the Minimal Models from phi31 ; It is known that any minimal model Mp receives along its phi31 irrelevant direction two massless integrable flows one from Mp1 perturbed by phi13, the other from Zp1 parafermionic model perturbed by its generating parafermion field. By comparing Thermodynamic Bethe Ansatz data and predictions'' of infrared Conformal Perturbation Theory we show that these two flows are received by Mp with opposite coupling constants of the phi31 irrelevant perturbation. Some comments on the massless S matrices of these two flows are added.

Exact Solution of 1matrix Model ; I review my new method for solving general 1matrix models by expanding in N1 without taking a physical continuum limit. Using my method, each coefficient of the free energy in the genus expansion is exactly computable. One can include physical information in a function which is uniquely specified by the action of the model. My method gives completely the same result with the usual one if the physical fine tuning is done and the leading singular terms are extracted. I also calculate in the genus three case and confirm the validity of my method.

A comment on freefermion conditions for lattice models in two and more dimensions ; We analyze freefermion conditions on vertex models. We show by examining examples of vertex models on square, triangular, and cubic lattices how they amount to degeneration conditions for known symmetries of the Boltzmann weights, and propose a general scheme for such a process in two and more dimensions.

Gauged NJL model at strong curvature ; We investigate the gauged NJLmodel in curved spacetime using the RG formulation and the equivalency with the gauge HiggsYukawa model in a modified 1Nc expansion. The strong curvature induced chiral symmetry breaking is found in the nonperturbative RG approach presumably equivalent to the ladder SchwingerDyson equations. Dynamically generated fermion mass is explicitly calculated and inducing of Einstein gravity is briefly discussed. This approach shows the way to the nonperturbative study of the dynamical symmetry breaking at external fields.

Higher spin constraints and the super Winftyover 2oplus W1inftyover 2 algebra in the super eigenvalue model ; We show that the partition function of the super eigenvalue model satisfies an infinite set of constraints with even spins s4,6,cdots,infty. These constraints are associated with half of the bosonic generators of the super left Winfty over 2oplus W1inftyover 2right algebra. The simplest constraint s4 is shown to be reducible to the super Virasoro constraints, previously used to construct the model. All results hold for finite N.

Comments on Gepner Models and Type I Vacua in String Theory ; We construct open descendants of Gepner models, concentrating mainly on the sixdimensional case, where they give type I vacua with rich patterns of ChanPaton symmetry breaking and various numbers of tensor multiplets, including zero. We also relate the models in D 10 without open sectors, recently found by other authors, to the generalized Kleinbottle projections allowed by the crosscap constraint.

Gravitational dressing of massive soliton theories ; The massive soliton theories describe integrable perturbations of WZW cosets as generalized multicomponent sineGordon models. We study their coupling to 2dim gravity in the conformal gauge and show that the resulting models can be interpreted as conformal nonAbelian Toda theories when a certain algebraic condition is satisfied. These models, however, do not provide quantum mechanically consistent string backgrounds in the case the underlying WZW constraints are first solved classically.

On Bosonic, Fermionic and Mixed Supersymmetric 2Dimensional Integrable Models ; It is shown that supersymmetric integrable models in two dimensions, both relativistic i.e. superToda type theories and nonrelativistic reductions of superKP hierarchies can be associated to general Poissonbrackets structures given by superaffinizations of any bosonic Lie or any superLie algebra. This result allows enlarging the set of supersymmetric integrable models, which are no longer restricted to the subclass of superaffinizations of purely fermionic superLie algebras that is admitting fermionic simple roots only.

Analytic regularization of the Yukawa Model at Finite Temperature ; We analyse the oneloop fermionic contribution for the scalar effective potential in the temperature dependent Yukawa model. In order to regularize the model a mix between dimensional and analytic regularization procedures is used. We find a general expression for the fermionic contribution in arbitrary spacetime dimension. It is found that in D3 this contribution is finite.

Some chiral rings of N2 discrete superconformal series induced by SL2 degenerate conformal field theories ; By generalizing a fermionic construction, a natural relation is found between SL2 degenerate conformal field theories and some N2 discrete superconformal series. These nonunitary models contain, as a subclass, N2 minimal models. The construction permits one to investigate the properties of chiral operators in the N2 models. A chiral ring reveals a close connection with underlying quantum group structures.

Logarithmic Yangians in WZW models ; A new action of the Yangians in the WZW models is displayed. Its structure is generic and level independent. This Yangian is the natural extension at the conformal point of the one unravelled in massive theories with current algebras. Expectingly, this new symmetry of WZW models will lead to a deeper understanding of the integrable structure of conformal field theories and their deformations.

Supersymmetric NambuJonaLasinio Model in an External Gravitational Field ; We investigate the effect of an external gravitational fields to the chiral symmetry breaking in the SUSY supersymmetric NJL NambuJonaLasinio model nonminimally interacting with external supergravity. Evaluating the effective potential in the leading order of the 1Ncexpansion and in the linear curvature approximation it is found the possibility of the chiral symmetry breaking in the SUSY NJL model in an external gravitational fields. In the broken phase the dynamically generated mass is analytically and numerically calculated.

Super YangMills in 11,3 Dimensions ; A supersymmetric YangMills system in 11,3 dimensions is constructed with the aid of two mutually orthogonal null vectors which naturally arise in a generalized spacetime superalgebra. An obstacle encountered in an attempt to extend this result to beyond 14 dimensions is described. A null reduction of the 11,3 model is shown to yield the known super YangMills model in 10,2 dimensions. An 8,8 supersymmetric super YangMills system in 3,3 dimensions is obtained by an ordinary dimensional reduction of the 11,3 model, and it is suggested there may exist a superbrane with 3,3 dimensional worldvolume propagating in 11,3 dimensions.

Vacuum properties of a NonLocal ThirringLike Model ; We use pathintegral methods to analyze the vacuum properties of a recently proposed extension of the Thirring model in which the interaction between fermionic currents is nonlocal. We calculate the exact ground state wave functional of the model for any bilocal potential, and also study its longdistance behavior. We show that the ground state wave functional has a general factored Jastrow form. We also find that it posess an interesting symmetry involving the interchange of densitydensity and currentcurrent interactions.

Equivalent bosonic theory for the massive Thirring model with nonlocal interaction ; We study, through pathintegral methods, an extension of the massive Thirring model in which the interaction between currents is nonlocal. By examining the massexpansion of the partition function we show that this nonlocal massive Thirring model is equivalent to a certain nonlocal extension of the sineGordon theory. Thus, we establish a nonlocal generalization of the famous Coleman's equivalence. We also discuss some possible applications of this result in the context of onedimensional strongly correlated systems and finitesize Quantum Field Theories.

On thermal phase structure of deformed GrossNeveu model ; We illustrate the phase structure of a deformed twodimensional GrossNeveu model which is defined by undeformed field contents plus deformed Pauli matrices. This deformation is based on two motives to find a more general polymer model and to estimate how qdeformed field theory affects on its effective potential. There found some regions where chiral symmetry breaking and restoration take place repeatedly as temperature increasing.

Target Space Duality for 0,2 Compactifications ; The moduli spaces of two 0,2 compactifications of the heterotic string can share the same LandauGinzburg model even though at large radius they look completely different. It was argued that such a pair of 0,2 models might be connected via a perturbative transition at the LandauGinzburg point. Situations of this kind are studied for some explicit models. By calculating the exact dimensions of the generic moduli spaces at large radius, strong indications are found in favor of a different scenario. The two moduli spaces are isomorphic and complex, Kahler and bundle moduli get exchanged.

Thirring Model in Lower Dimensions Nonperturbative Approaches ; A reformulation of the Thirring model as a gauge theory on both continuum spacetime and discretized lattice is reviewed. In 11 dimensions, our result reproduces consistently the bosonization of the massless Thirring model. In 21 dimensions, the analysis by use of SchwingerDyson equation is shown to exhibit dynamical fermion mass generation when the number N of fourcomponent fermions is less than the critical value Ncr 1283pi2.

Quantum Integrable Systems Basic Concepts and Brief Overview ; An overview of the quantum integrable systems QIS is presented. Basic concepts of the theory are highlighted stressing on the unifying algebraic properties, which not only helps to generate systematically the representative Lax operators of different models, but also solves the related eigenvalue problem in an almost model independent way. Difference between the approaches in the integrable ultralocal and nonultralocal quantum models are explained and the interrelation between the QIS and other subjects are focussed on.

Can Pions Smell'' 4D, N 1 Supersymmetry ; We show how the usual chiral perturbation theory description of phenomenological pion physics admits an interpretation as a lowenergy stringlike model associated with QCD. By naive and straightforward generalization within the context of a new class of supersymmetrical models, it is shown that this stringlike structure admits a 4D, N 1 supersymmetrical extension. The presence of a WZNW term in the model implies modifications of certain higher order processes involving the ordinary SU3 pion octet.

Particle production in string cosmology models ; We compute spectra of particles produced during a dilatondriven kinetic inflation phase within string cosmology models. The resulting spectra depend on the parameters of the model and on the type of particle and are quite varied, some increasing and some decreasing with frequency. We use an approximation scheme in which all spectra can be expressed in a nice symmetric form, perhaps hinting at a deeper symmetry of the underlying physics. Our results may serve as a starting point for detailed studies of relic abundances, dark matter candidates, and possible sources of large scale anisotropy.

On the Construction of Zero Energy States in Supersymmetric Matrix Models ; For the SUN invariant supersymmetric matrix model related to membranes in 4 spacetime dimensions, the general solution to the equations QdaggerPsi0 Qchi 0 is determined for N odd. For any such bosonic solution of QdaggerPsi0, a fermionic Phi is found that formally satisfies QdaggerPhiPsi. For the analogous model in 11 dimensions the solution of QdaggerPsi0 QPsi0 is outlined.

Zero curvature representation for classical lattice sineGordon equation via quantum Rmatrix ; Local Moperators for the classical sineGordon model in discrete spacetime are constructed by convolution of the quantum trigonometric 4times4 Rmatrix with certain vectors in its quantum space. Components of the vectors are identified with taufunctions of the model. This construction generalizes the known representation of Moperators in continuous time models in terms of Lax operators and classical rmatrix.

Degeneracy Structure of the CalogeroSutherland Model an Algebraic Approach ; The degeneracy structure of the eigenspace of the Nparticle CalogeroSutherland model is studied from an algebraic point of view. Suitable operators satisfying SU2 algebras and acting on the degenerate eigenspace are explicitly constructed for the two particle case and then appropriately generalized to the Nparticle model. The raising and lowering operators of these algebras connect the states, in a subset of the degenerate eigenspace, with each other.

A Matrix Model Solution of Hirota Equation ; We present a hermitian matrix chain representation of the general solution of the Hirota bilinear difference equation of three variables. In the large N limit this matrix model provides some explicit particular solutions of continuous differential Hirota equation of three variables. A relation of this representation to the eigenvalues of transfer matrices of 2D quantum integrable models is discussed.

Superparticles, pForm Coordinates and the BPS Condition ; A model for n superparticles in dn,n dimensions is studied. The target space supersymmetry involves a product of n momentum generators, and the action has nn12 local bosonic symmetries and n local fermionic symmetries. The precise relation between the symmetries presented here and those existing in the literature is explained. A new model is proposed for superparticles in arbitrary dimensions where coordinates are associated with all the pform charges occuring in the superalgebra. The model naturally gives rise to the BPS condition for the charges.

Effectiveness of Onedimensional gas models for black holes ; A onedimensional gas model has been constructed and shown to provide correct expressions for entropies for extremal and nearextremal BTZ black holes. Recently suggested boosting of black strings is used to compute the entropy for the Schwarzschild black hole also from this gas model.

Matrix Theory from Schild Action ; Starting from the Schild action for membrane, we present an alternative formulation of Matrix Theory. First of all, we construct the Schild action for general bosonic pbrane which is classically equivalent to the NambuGoto action for pbrane. Next, based on the constraint obtained from the variational equation for the auxiliary field in the case of p 2 membrane, we construct a new matrix model which is closely related to the matrix model of Mtheory as developed by Banks, Fischler, Shenker and Susskind BFSS. Our present formulation is a natural extension of the construction of type IIB matrix model by Yoneya to the case of Mtheory.

A Solvable Model of TwoDimensional DilatonGravity Coupled to a Massless Scalar Field ; We present a solvable model of twodimensional dilatongravity coupled to a massless scalar field. We locally integrate the field equations and briefly discuss the properties of the solutions. For a particular choice of the coupling between the dilaton and the scalar field the model can be interpreted as the twodimensional effective theory of 21 cylindrical gravity minimally coupled to a massless scalar field.

A Note on 0,2 Models on CalabiYau Complete Intersections ; In the class of 0,2 heterotic compactifications which has been constructed in the framework of gauged linear sigma models the CalabiYau varieties X are realized as complete intersections of hypersurfaces in toric varieties IP and the corresponding gauge bundles or more generally gauge sheaves E are defined by some short exact sequences. We show that there is yet another degree of freedom in resolving singularities in such models which is related to the possible choices of nef partitions of the anticanonical divisors in Gorenstein Fano toric varieties IP.

A New Class of Integrable Models of 11 Dimensional Dilaton Gravity Coupled to Scalar Matter ; Integrable models of 11 dimensional gravity coupled to scalar and vector fields are briefly reviewed. A new class of integrable models with nonminimal coupling to scalar fields is constructed and discussed.

Exactly solvable dynamical systems in the neighborhood of the Calogero model ; The Hamiltonian of the Nparticle Calogero model can be expressed in terms of generators of a Lie algebra for a definite class of representations. Maintaining this Lie algebra, its representations, and the flatness of the Riemannian metric belonging to the second order differential operator, the set of all possible quadratic Lie algebra forms is investigated. For N3 and N4 such forms are constructed explicitly and shown to correspond to exactly solvable Sutherland models. The results can be carried over easily to all N.

String Representation of Field Correlators in the Dual Abelian Higgs Model ; By making use of the path integral duality transformation, we derive the string representation for the partition function of an extended Dual Abelian Higgs Model containing gauge fields of external currents of electrically charged particles. By the same method, we obtain the corresponding representations for the generating functionals of gauge field and monopole current correlators. In the case of bilocal correlators, the obtained results are found to be in agreement with the dual Meissner scenario of confinement and with the Stochastic Model of the QCD vacuum.

Schroedinger Representation of CPN Model for Large N ; We examine the 11 dimensional CPN model in the large N limit by using the Schroedinger representation. Starting from the Hamiltonian analysis of the model, we present the variational gap equation resulting from the Gaussian trial wave functional. The renormalization of the theory is performed with insertion of mass and energy counterterms, and the dynamical generation of mass and the energy eigenvalue are derived.

Observational Tests of Instanton Cosmology ; A new cosmological model leads to testable predictions that are different from those of both standard cosmology and models with a cosmological constant. The prediction that q00 is the same as in other coasting universe'' models, but arises without the need for any exotic form of matter or other ad hoc assumptions.

String Fields and the Standard Model ; The CremmerScherk mechanism is generalised in a nonAbelian context. In the presence of the Higgs scalars of the standard model it is argued that fields arising from the low energy effective string action may contribute to the mass generation of the observed vector bosons that mediate the electroweak interactions and that future analyses of experimental data should consider the possibility of string induced radiative corrections to the Weinberg angle coming from physics beyond the standard model.

Good Propagation'' Constraints on Dual Invariant Actions in Electrodynamics and on Massless Fields ; We present some consequences of nonanomalous propagation requirements on various massless fields. Among the models of nonlinear electrodynamics we show that only Maxwell and BornInfeld also obey duality invariance. Separately we show that, for actions depending only on the Fmn2 invariant, the permitted models have L sim sqrt1 F2. We also characterize acceptable vectorscalar systems. Finally we find that wide classes of gravity models share with Einstein the null nature of their characteristic surfaces.

D4, N1 Supersymmetric HenneauxKnaepen Models ; We construct N1 supersymmetric versions of fourdimensional FreedmanTownsend models and generalizations thereof found recently by Henneaux and Knaepen, with couplings between 1form and 2form gauge potentials. The models are presented both in a superfield formulation with linearly realized supersymmetry and in WZ gauged component form. In the latter formulation the supersymmetry transformations are nonlinear and do not commute with all the gauge transformations. Among others, our construction yields N1 counterparts of recently found N2 supersymmetric gauge theories involving vectortensor multiplets with gauged central charge.

Lightcone formulation and spin spectrum of noncritical fermionic string ; A free fermionic string quantum model is constructed directly in the lightcone variables in the range of dimensions 1d10. It is shown that after the GSO projection this model is equivalent to the fermionic massive string and to the noncritical RammondNeveuSchwarz string. The spin spectrum of the model is analysed. For d4 the character generating functions is obtained and the particle content of first few levels is numerically calculated.

Gravitating monopoles and black holes in EinsteinBornInfeldHiggs model ; We find static spherically symmetric monopoles in EinsteinBornInfeldHiggs model in 31 dimensions. The solutions exist only when a parameter a related to the strength of Gravitational interaction does not exceed certain critical value. We also discuss magnetically charged non Abelian black holes in this model. We analyse these solutions numerically.

Gravitating dyons and dyonic black holes in EinsteinBornInfeldHiggs model ; We find static spherically symmetric dyons in EinsteinBornInfeldHiggs model in 31 dimensions. The solutions share many features with the gravitating monopoles in the same model. In particular, they exist only up to some critical value of a parameter a related to the strength of the gravitational interaction. We also study dyonic nonAbelian black holes. We analyse these solutions numerically.