Doron Gepner

• PhD
• Professor (Full) at Weizmann Institute of Science

A bstract This paper represents a continuation of our previous work, where the Boltzmann weights (BWs) for several Interaction-Round-the Face (IRF) lattice models were computed using their relation to rational conformal field theories. Here, we focus on deriving solutions for the Boltzmann weights of the Interaction-Round the Face lattice model, sp...

This paper represents a continuation of our previous work, where the Bolzmann weights (BWs) for several Interaction-Round-the Face (IRF) lattice models were computed using their relation to rational conformal field theories. Here, we focus on deriving solutions for the Boltzmann weights of the Interaction-Round the Face lattice model, specifically...

We investigate here the deformations of Berglund H\"ubsch loop and chain mirrors where the original manifolds are defined in the same weighted projective space. We show that the deformations are equivalent by two methods. First, we map directly the two models to each other and show that the deformations are the same for $79$ "Good" models, but not...

Interaction-Round the Face (IRF) models are two-dimensional lattice models of statistical mechanics defined by an affine Lie algebra and admissibility conditions depending on a choice of representation of that affine Lie algebra. Integrable IRF models, i.e., the models the Boltzmann weights of which satisfy the quantum Yang-Baxter equation, are of...

Interaction-Round the Face (IRF) models are two-dimensional lattice models of statistical mechanics defined by an affine Lie algebra and admissibility conditions depending on a choice of representation of that affine Lie algebra. Integrable IRF models, i.e., the models the Boltzmann weights of which satisfy the quantum Yang-Baxter equation, are of...

In this article we consider a question: what is the relation between two Calabi-Yau manifolds of two different Berglund--Hubsch types if they appear as hyper--surfaces in the quotient of the same weighted projective space. We show that that these manifolds are connected by a special change of coordinates, which we call the resonance transformation.

We study the large class of solvable lattice models, based on the data of conformal field theory. These models are constructed from any conformal field theory. We consider the lattice models based on affine algebras described by Jimbo et al, for the algebras ABCD and by Kuniba et al for G 2. We find a general formula for the crossing multipliers of...

Hatayama et al. described generalized Rogers–Ramanujan (GRR) expressions for the string functions of the singlet representation of twisted affine algebras. We give here such GRR expressions for some non-singlet string functions. In the case of the algebra A2(2), this gives all the string functions. We verify these expressions using Freudenthal–Kac...

Hatayama et al. described generalized Rogers--Ramanujan (GRR) expressions for the string functions of the singlet representation of twisted affine algebras. We give here such GRR expressions for some non-singlet string functions. In the case of the algebra $A_2^{(2)}$ this gives all the string functions. We verify these expressions using Freudentha...

We consider the lattice models based on affine algebras described by Jimbo et al., for the algebras ABCD and by Kuniba et al. for G2. We find a general formula for the crossing multipliers of these models. It is shown that these crossing multipliers are also given by the principally specialized characters of the model in question. Therefore we conj...

We conjecture the inversion relations for thermalized solvable interaction round the face (IRF) two dimensional lattice models. We base ourselves on an ansatz for the Baxterization described in the 90's. We solve these inversion relations in the four main regimes of the models, to give the free energy of the models, in these regimes. We use the met...

We study the fused SU(2) models put forward by Date et al, that are a series of models with arbitrary number of blocks, which is the degree of the polynomial equation obeyed by the Boltzmann weights. We demonstrate by a direct calculation that a version of Birman–Murakami–Wenzl (BMW) algebra [1, 2] is obeyed by five, six and seven blocks models, co...

Solvable vertex models in two dimensions are of importance in conformal field theory, phase transitions and integrable models. We consider here the Dn spin vertex models, for n which is odd. The models involve also the anti–spinor representation. We describe here the Boltzmann weights for these representations using crossing symmetry from the previ...

Solvable vertex models in two dimensions are of importance in conformal field theory, phase transitions and integrable models. We consider here the $D_n$ spin vertex models, for $n$ which is odd. The models involve also the anti--spinor representation. We describe here the Boltzmann weights for these representations using crossing symmetry from the...

We conjecture the inversion relations for thermalized solvable interaction round the face (IRF) two dimensional lattice models. We base ourselves on an ansatz for the Baxterization described by the author in the 90's. We solve these inversion relations in the four main regimes of the models, to give the free energy of the models, in these regimes....

We describe the Boltzmann weights of the Dk algebra spin vertex models. Thus, we find the SO(N) spin vertex models, for any N, completing the Bk case found earlier. We further check that the real (self–dual) SO(N) models obey quantum algebras, which are the Birman–Murakami–Wenzl (BMW) algebra for three blocks, and certain generalizations, which inc...

We describe the Boltzmann weights of the $D_k$ algebra spin vertex models. Thus, we find the $SO(N)$ spin vertex models, for any $N$, completing the $B_k$ case found earlier. We further check that the real (self-dual) SO$(N)$ models obey quantum algebras, which are the Birman-Murakami-Wenzl (BMW) algebra for three blocks, and certain generalization...

We construct new solvable vertex models based on the spin representation of the Lie algebra Bk. We use these models to study the algebraic structure underlying such vertex theories. We show that all the Bk spin vertex models obey a version of the BMW algebra along with extra relations that are called n–CB (conformal braiding) algebras. These algebr...

We construct new solvable vertex models based on the spin representation of the Lie algebra $B_k$. We use these models to study the algebraic structure underlying such vertex theories. We show that all the $B_k$ spin vertex models obey a version of the BMW algebra along with extra relations that are called $n$--CB (conformal braiding) algebras. The...

We study the fused $SU(2)$ models put forward by Date et al., which is a series of models with arbitrary number of blocks, which is the degree of the polynomial equation obeyed by the Boltzmann weights. We demonstrate by a direct calculation that a version of BMW (Birman--Murakami--Wenzl) algebra is obeyed by five, six and seven blocks models, esta...

A bstract We study the algebras underlying solvable lattice models of the type fusion interaction round the face (IRF). We propose that the algebras are universal, depending only on the number of blocks, which is the degree of polynomial equation obeyed by the Boltzmann weights. Using the Yang-Baxter equation and the ansatz for the Baxterization of...

We study the algebras underlying solvable lattice models of the type fusion interaction round the face (IRF). We propose that the algebras are universal, depending only on the number of blocks, which is the degree of polynomial equation obeyed by the Boltzmann weights. Using the Yang--Baxter equation and the ansatz for the Baxterization of the mode...

A bstract We treat here interaction round the face (IRF) solvable lattice models. We study the algebraic structures underlining such models. For the three block case, we show that the Yang Baxter equation is obeyed, if and only if, the Birman-Murakami-Wenzl (BMW) algebra is obeyed. We prove this by an algebraic expansion of the Yang Baxter equation...

Birman–Murakami–Wenzl (BMW) algebra was introduced in connection with knot theory. We treat here interaction round the face solvable (IRF) lattice models. We assume that the face transfer matrix obeys a cubic polynomial equation, which is called the three block case. We prove that the three block theories all obey the BMW algebra. We exemplify this...

We treat here interaction round the face (IRF) solvable lattice models. We study the algebraic structures underlining such models. For the three block case, we show that the Yang Baxter equation is obeyed, if and only if, the Birman--Murakami--Wenzl (BMW) algebra is obeyed. We prove this by an algebraic expansion of the Yang Baxter equation (YBE)....

Birman--Murakami--Wenzl (BMW) algebra was introduced in connection with knot theory. We treat here interaction round the face solvable (IRF) lattice models. We assume that the face transfer matrix obeys a cubic polynomial equation, which is called the three block case. We prove that the three block theories all obey the BMW algebra. We exemplify th...

The characters of parafermionic conformal field theories are given by the string functions of affine algebras, which are either twisted or untwisted algebras. Expressions for these characters as generalized Rogers–Ramanujan algebras have been established for the untwisted affine algebras. However, we study the identities for the string functions of...

The characters of parafermionic conformal field theories are given by the string functions of affine algebras, which are either twisted or untwisted algebras. Expressions for these characters as generalized Rogers Ramanujan algebras have been established for the untwisted affine algebras. However, we study the identities for the string functions of...

It was shown many years ago by Dijkgraaf, Velinde, and Verlinde for two-dimensional topological conformal field theory and more recently for the non-critical String theory that some models of these two types can be solved using their connection to the special case of Frobenius manifolds—the so-called Saito Frobenius manifolds connected to a deforme...

A GRR expression for the characters of $A$-type parafermions has been a long standing puzzle dating back to conjectures made regarding some of the characters in the 80's. Not long ago we have put forward such GRR type identities describing any of the level two $ADE$-type generalized parafermions characters at any rank. These characters are the stri...

It was shown in \cite{DVV} for $2d$ topological Conformal field theory (TCFT) \cite{EY,W} and more recently in \cite{BSZ}-\cite{BB2} for the non-critical String theory \cite{P}-\cite{BAlZ} that a number of models of these two types can be exactly solved using their connection with the Frobenius manifold (FM) structure introduced by Dubrovin\cite{Du...

We discuss our conjecture for simply laced Lie algebras level two string functions of mark one fundamental weights and prove it for the algebra. To prove our conjecture we introduce q-diagrams and examine the diagrammatic interpretations of known identities by Euler, Cauchy, Heine, Jacobi and Ramanujan. Interestingly, the diagrammatic approach impl...

We discuss our conjecture for simply laced Lie algebras level two string functions of mark one fundamental weights and prove it for the $SO(2r)$ algebra. To prove our conjecture we introduce $q$-diagrams and examine the diagrammatic interpretations of known identities by Euler, Cauchy, Heine, Jacobi and Ramanujan. Interestingly, the diagrammatic ap...

We study cosets of the type $H_l/U(1)^r$, where $H$ is any Lie algebra at level $l$ and rank $r$. These theories are parafermionic and their characters are related to the string functions, which are generating functions for the multiplicities of weights in the affine representations. An identity for the characters is described, which apply to all t...

The level two string functions are calculated exactly for all simply laced Lie algebras, using a ladder coset construction. These are the characters of cosets of the type $G/U(1)^r$, where $G$ is the algebra at level two and $r$ is its rank. This coset is a theory of generalized parafermions. A conjectured Rogers Ramanujan type identity is describe...

New heterotic string theories in four dimensions are constructed by tensoring a nonstandard SCFT along with some minimal SCFT's. All such theories are identified and their particle generation number is found. We prove that from the infinite number of new heterotic string theories only the {6} theory predicts three generations as seen in nature whic...

The space of (2,0) models is of particular interest among all heterotic-string models because it includes the models with the minimal $SO(10)$ unification structure, which is well motivated by the Standard Model of particle physics data. The fermionic $\mathbb{Z}_2\times \mathbb{Z}_2$ heterotic-string models revealed the existence of a new symmetry...

Every conformal field theory has the symmetry of taking each field to its adjoint. We consider here the quotient (orbifold) conformal field theory obtained by twisting with respect to this symmetry. A general method for computing such quotients is developed using the Coulomb gas representation. Examples of parafermions, SU(2) current algebra and th...

AGT correspondence and its generalizations attracted a great deal of attention recently. In particular it was suggested that $U(r)$ instantons on $R^4/Z_p$ describe the conformal blocks of the coset ${\cal A}(r,p)=U(1)\times sl(p)_r\times {sl(r)_p\times sl(r)_n\over sl(r)_{n+p}}$, where $n$ is a parameter. Our purpose here is to describe Generalize...

Nonstandard parafermions are built and their central charges and dimensions are calculated. We then construct new N=2 superconformal field theories by tensoring the parafermions with a free boson. We study the spectrum and modular transformations of these theories. Superstring and heterotic strings in four dimensions are then obtained by tensoring...

We propose a generalization of the Zamolodchikov-Fateev parafermions which are abelian, to nonabelian groups. The fusion rules are given by the tensor product of representations of the group. Using Vafa equations we get the allowed dimensions of the parafermions. We find for simple groups that the dimensions are integers. For cover groups of simple...

A sort of calculus is developed to find the chiral algebras of N = 2 superconformal interacting bosonic models. Many examples are discussed. It is shown that the algebras share a common structure, which we call almost Landau Ginzburg. For one or two generators, the number of relations is equal to the number of generators and they are algebraically...

Using Verlinde formula and the symmetry of the modular matrix we describe an algorithm to find all conformal field theories with low number of primary fields. We employ the algorithm on up to eight primary fields. Four new conformal field theories are found which do not appear to come from current algebras. This supports evidence to the fact that r...

It was established before that fusion rings in a rational conformal field theory (RCFT) can be described as rings of polynomials, with integer coefficients, modulo some relations. We use the Galois group of these relations to obtain a local set of equations for the points of the fusion variety. These equations are sufficient to classify all the RCF...

We express the discriminant of the polynomial relations of the fusion ring, in any conformal field theory, as the product of the rows of the modular matrix to the power −2. The discriminant is shown to be an integer, always, which is a product of primes which divide the level. Detailed formulas for the discriminant are given for all WZW conformal f...

We develop an algebraic approach to solvable lattice models based on a chain of algebras obeyed by the models. In each subalgebra we use a unit, giving a chain of ideals. Thus, we divide the models into distinct sectors which do not mix. This method gives the usual Bethe anzats results in cases it is known, but generalizes it to non integrable mode...

Using the inversion relation method, we calculate the ground-state energy for the lattice integrable models, based on baxterization of multicoloured generalization of Temperley–Lieb algebras. The simplest vertex model is analysed and found to have a mass gap.

We study intersection of $N_c$ color D4 branes with $N_f$ Dp-branes and anti-Dp branes in the strong coupling limit in the probe approximation. The resulting model has $U(N_f)\times U(N_f)$ global symmetry. We see an $n$ dimensional theory for $n$ overlapping directions between color and flavor branes. At zero temperature we do see the breakdown of...

We express the discriminant of the polynomial relations of the fusion ring, in any conformal field theory, as the product of the rows of the modular matrix to the power -2. The discriminant is shown to be an integer, always, which is a product of primes which divide the level. Detailed formulas for the discriminant are given for all WZW conformal f...

We introduce a Monte–Carlo simulation approach to thermodynamic Bethe ansatz (TBA). We exemplify the method on one-particle integrable models, which include a free boson and a free fermions systems along with the scaling Lee–Yang model (SLYM). It is confirmed that the central charges and energies are correct to a very good precision, typically 0.1%...

We have found the solution to the back reaction of putting a stack of coincident D3- and D5-branes in R3,1×M6R3,1×M6, where M6M6 is constructed from an infinite class of Sasaki–Einstein spaces, L(p,q,r)L(p,q,r). The non-zero fluxes associated to 2-form potential suggests the presence of a non-contractible 2-cycle in this geometry. The radial part o...

Recently, I have defined the so called PDF's (prime distribution factors) which govern the distribution of prime numbers of the type $p,p+a_i$ being all primes up to some number $n$. It was shown that the PDF's are expressible in terms of the basic PDF's which are defined as $a_i-a_j$ or $a_i$ being composed of primes which are less or equal to the...

The probability of finding a prime multiplet, i.e., a sequence of primes $p$ and $p+a_i$, $i=1... m$, being all primes where $p$ is some prime less than the integer $n$ is naively $1/log(n)^{m+1}$. It is shown that, in reality, it is proportional to this probability by a constant factor which depends on $a_i$ and $m$ but not on $n$, for large $n$....

We study a family of interacting bosonic representations of the N=2 superconformal algebra. These models can be tensored with a conjugate theory to give the free theory. We explain how to use free fields to study interacting fields and their dimensions, and how we may identify different free fields as representing the same interacting field. We sho...

SW(3/2,2) superconformal algebra is W algebra with two Virasoro operators. The Kac determinant is calculated and the complete list of unitary representations is determined. Two types of extensions of SW(3/2,2) algebra are discussed. A new approach to construction of W algebras from rational conformal field theories is proposed.

Pseudoaffine theories are characterized by formal replacement of the level to the fractional number: $k\to\frac{k}{q}$, where $q$ is integer strange to $k(g+k)$ ($g$ - dual Coxeter number). An example of "forbidden" $q$ is considered (SU(2), $q=2$). The fusions of obtained theory are similar to the affine ones. Spectra of minimal models are calcula...

Pseudo conformal field theories are theories with the same fusion rules, but with different modular matrix as some conventional field theory. One of the authors defined these and conjectured that, for bosonic systems, they can all be realized by some actual RCFT, which is of free bosons. We complete the proof here by treating the non diagonal autom...

Pseudo conformal field theories are theories with the same fusion rules, but with different modular matrix as some conventional field theory. One of the authors defined these and conjectured that, for bosonic systems, they can all be realized by some actual RCFT, which is of free bosons. We complete the proof here by treating the non diagonal autom...

Some time ago, conformal data with affine fusion rules were found. Our purpose here is to realize some of these conformal data, using systems of free bosons and parafermions. The so constructed theories have an extended $W$ algebras which are close analogues of affine algebras. Exact character formulae is given, and the realizations are shown to be...

A general phase diagram for isotropic antiferromagnetic chains has been proposed recently, using conformal field theory. This is developed further to predict the spectrum of finite chains, including logarithmic corrections. These predictions are tested against Bethe ansatz and exact diagonalisation results for various Hamiltonians with s=1/2, 1 and...

For each lattice one can define a free boson theory propagating on the corresponding torus. We give an alternative definition where one employs any automorphism of the group $M^*/M$. This gives a wealth of conformal data, which we realize as some bosonic theory, in all the `regular' cases. We discuss the generalization to affine theories. As a bypr...

We present fermionic sum representation for the general Virasoro character of the unitary minimal superconformal series (N = 1). An example of the corresponding “finitizated” identities relating corner transfer matrix polynomials with fermionic companions is considered. These identities in the thermodynamic limit lead to the generalized Rogers-Rama...

The initial classification of fusion rules have shown that rational conformal field theory is very limited. In this paper we study the fusion rules of extend ed current algebras. Explicit formulas are given for the S matrix and the fusion rules, based on the full splitting of the fixed point fields. We find that in s ome cases sensible fusion rules...

The fusion rules and modular matrix of a rational conformal field theory obey a list of properties. We use these properties to classify rational conformal field theories with not more than six primary fields and small values of the fusion coefficients. We give a catalogue of fusion rings which can arise for these field theories. It is shown that al...

We present fermionic sum representation for the general Virasoro character of the unitary minimal superconformal series ($N=1$). Example of the corresponding ``finitizated" identities relating corner transfer matrix polynomials with fermionic companions is considered. These identities in the thermodynamic limit lead to the generalized Rogers-Ramanu...

We revisit the solvable lattice models described by Andrews Baxter and Forrester and their generalizations. The expressions for the local state probabilities were shown to be related to characters of the minimal models. We recompute these local state probabilities by a different method. This yields generalized Rogers Ramanujan identities, some of w...

We study here the spectrum of soliton scattering theories based on interaction round the face lattice models. We take for the admissibility condition the fusion rules of each of the simple Lie algebras. It is found that the mass spectrum is given by that of the corresponding Toda theory, or, that the mass ratios of the different kinks in the model...

Recently, a class of interaction round the face (IRF) solvable lattice models were introduced, based on any rational conformal field theory (RCFT). We investigate here the connection between the general solvable IRF models and the fusion ones. To this end, we introduce an associative algebra associated to any graph, as the algebra of products of th...

Recently, a class of solvable interaction round the face lattice models (IRF) were constructed for an arbitrary rational conformal field theory (RCFT) and an arbitrary field in it. The Boltzmann weights of the lattice models are related in the extreme ultra violet limit to the braiding matrices of the rational conformal field theory. In this note w...

RSOS models based on the Lie algebras $B_m$, $C_m$ and $D_m$ are derived from the braiding of conformal field theory. This gives the first systematic derivation of these models earlier described by Jimbo et al. The general two field Boltzmann weights associated to any RCFT are described, giving in particular the off critical thermalized Boltzmann w...

Recently, string theory on Calabi--Yau manifolds was constructed and was shown to be a fully consistent, space--time supersymmetric string theory. The physically interesting case is the case of three generations. Intriguingly, it appears at the present that there is a unique manifold which gives rise to three generations. We describe in this paper...

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 $SU(N)_k$ with the fundamental are evaluated and are used as exa...

The connection between rational conformal field theory (RCFT), N=2 massive supersymmetric field theory, and solvable interaction round the face (IRF) lattice models is explored here. Specifically, one identifies the fusion rings with the chiral rings. The theories so obtained are conjectured, and largely shown to be integrable, based on a variety o...

The connection between Rational Conformal Field Theory (RCFT), $N=2$ massive supersymmetric field theory, and solvable Interaction Round the Face (IRF) lattice models is explored here. Specifically, one identifies the fusion rings with the chiral rings. The theories so obtained are conjectured, and largely shown, to be integrable. A variety of exam...

The fusion of fields in a rational conformal field theory gives rise to a ring structure which has a very particular form. All such rings studied so far were shown to arise from some potentials. In this paper the fusion rings of the WZW models based on the symplectic group are studied. It is shown that they indeed arise from potentials which are de...

InN=2 string theory the chiral algebra expresses the generations and anti-generations of the theory and the Yukawa couplings among them and is thus crucial to the phenomenological properties of the theory. Also the connection with complex geometry is largely through the algebras. These algebras are systematically investigated in this paper. A solut...

The algebraic structure of fusion rings in rational conformal field theories is analyzed in detail in this paper. A formalism which closely parallels classical tools in the study of the cohomology of homogeneous spaces is developed for fusion rings, in general, and for current algebra theories, in particular. It is shown that fusion rings lead to a...

A family of interacting bosonic models is studied. A picture is suggested where each such conformal field theory is tensored with a conjugate one to give a free bosonic theory. It is shown that the lattice of the bosonic theory is determined in each case, and how the spectrum and correlation functions can be calculated. It is explained how flat dir...

The new N = 2 conformal field theories based on SU(n + 1)/SU(n) × U(1) recently constructed as G/H theories are shown to be equivalent to certain supersymmetric scalar field theories. The chiral fields and their structure constants are described for any scalar field theories. This allows the calculation of the Yukawa couplings 273 in any supersymme...

Starting from an arbitrary N = 2 superconformal field theory it is described how a fully consistent, space–time supersymmetric heterotic–like string theory in an even number of dimensions is constructed. Four dimensional theories which arise in this construction have a gauge group which contains E 8 × E 6 with chiral fermions in the 27 and ¯ 27 rep...

The fields appearing in G/H coset conformal field theories are shown to obey certain relations. These relations, in conjunction with the modular transformations imply a certain identification of fields. The use of these relations and identifications leads to the correct modular invariant spectrum of the theories. The consistency of this spectrum wi...

Recently, we have described string theories based on N = 2 superconformal theories. It was argued that all such string theories correspond to string propagation on Calabi-Yau manifolds. We compute here the Yukawa couplings for massless particles in the representation 27 of E6 (generations), in some examples, and show that the quasi-topological resu...

Space-time supersymmetric compactified string theories which obey spin and statistics, tachyon free, and modular invariant, are constructed by compactifying on arbitrary sums of N = 2 minimal superconformal models. Heterotic-type compactifications with realistic phemomenology are described. The theories offer a considerably simpler structure than s...

Possible unitary statistical models and SU(2) current algebra theories are classified up to certain “levels” of the Virasoro and Kac-Moody algebras. A connection that is found between the Virasoro and SU(2) Kac-Moody characters is used to generate unitary statistical models from the SU(2) theories. Using the “fusion rules” of the operator product a...

New conformal field theories are defined as a generalization of the vertex operator construction to arbitrary level, k, and arbitrary simple Lie algebra. Exact scaling dimensions and partition functions are given in terms of the string functions of affine algebra. The theories have a discrete symmetry group which is the root lattice modulo k times...

The partition functions of the parafermionic theories of Zamolodchikov and Fateev are computed in terms of the string functions of affine algebra. Conditions for modular invariance are given and a complete set of solutions is found. The partition functions in the presence of twisted boundary conditions are also given. All the solutions are shown to...

A variety of heterotic string compactifications on the K3 surface, manifolds of SU(3) holomony, and higher holomony manifolds, are solved exactly. An example of the quintic hypersurface in CP4 is worked out in detail. It is conjectured, and demonstrated in part, that any supersymmetric compactification of the heterotic string with an N=2 superconfo...

A large class of primary fields which appear at any level of the WZW theories (of types AN, BN, CN, DN, E6, and E7) are shown to posses simple power-like four-point functions. As a consequence, these fields, which are in 1-1 correspondence with the center of the covering group, may be written as symmetrized products of level one fields. The latter...

Modular invariance has recently emerged as a powerful tool in conformal field theory. In conjunction with the representation theory of infinite dimensional Lie algebras, the study of modular invariance gave the spectrum of several families of theories. These include the minimal conformal models (Cardy and others), WZW theories which describe string...

A number of issues concerning affine Lie algebras and string propagation on group manifolds are addressed. We show that a 1 + 1 dimensional quantum field theory which gives a realization of current algebra (for any non-abelian Lie group G) will always give rise to an “integrable” representation. It is known that string propagation on the group mani...

It is shown that a theory of strings on a nonsimply-connected group manifold has a soliton sector that is essential for modular invariance. A semiclassical analysis of this sector is used to reduce the problem of determining the representations of the Kac-Moody algebra that appear in the theory to the relatively easy task of finding the representat...

Using Witten's recently suggested non-abelian bosonization, we shoe that as a dynamical result of QCD in two dimensions, a Wess-Zumino chiral effective action describes exactly the low-lying mesons and baryons, which appear as solitons. Isospin content and mass formulae are given. QED2 is also discussed, and in the strong coupling limit we find an...

We show directly the connection between two- and four-dimensional soliton theories coupled to fermions, thus explaining the equality of their respective fractional charges. The dependence of these charges on the boundary conditions of the ``half fermions'' is also computed.

Non-integer charges on topological objects in the presence of fermions are further investigated. The connections with anomalous commutators is discussed. The reason for the identical results in two dimensional solitons and four dimensional monopoles is pointed out.

We present the bosonized hamiltonian for (QCD)2 with flavor. The bosonized theory has non local momentum dependent interactions. It is argued that the strong coupling static approximation is unacceptable.