u-Deformed WZW Model and Its Gauging

The chiral Wess-Zumino-Novikov-Witten (WZNW) model provides the simplest class of rational conformal field theories which exhibit a non-abelian braid-group statistics and an associated "quantum symmetry". The canonical derivation of the Poisson-Lie symmetry of the classical chiral WZNW theory (originally studied by Faddeev, Alekseev, Shatashvili and Gawedzki, among others) is reviewed along with subsequent work on a covariant quantization of the theory which displays its quan...

The present paper is revised copy of hep-th/9303087 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 Kac-Moody algebra are obtained. A characteristic property of the WZNW model is that it admits a higher spin linear realization of the extended affine Kac-Moody algebra which is equivalent to the corresponding higher spin nonlinear realization of the same...

Working directly on affine Lie groups, we construct several new formulations of the WZW model. In one formulation WZW is expressed as a one-dimensional mechanical system whose variables are coordinates on the affine Lie group. When written in terms of the affine group element, this formulation exhibits a two-dimensional WZW term. In another formulation WZW is written as a two-dimensional field theory, with a three-dimensional WZW term, whose fields are coordinates on the affi...

We briefly review the possible Poisson structures on the chiral WZNW phase space and discuss the associated Poisson-Lie groupoids. Many interesting dynamical r-matrices appear naturally in this framework. Particular attention is paid to the special cases in which these r-matrices satisfy the classical dynamical Yang-Baxter equation or its Poisson-Lie variant.

We show that O(2,2) transformation of SU(2) WZNW model gives rise to marginal deformation of this model by the operator $\int d^2 z J(z)\bar J(\bar z)$ where $J$, $\bar J$ are U(1) currents in the Cartan subalgebra. Generalization of this result to other WZNW theories is discussed. We also consider O(3,3) transformation of the product of an SU(2) WZNW model and a gauged SU(2) WZNW model. The three parameter set of models obtained after the transformation is shown to be the re...

We study the "topological gauged WZW model associated with $SU(2)/U(1)$",which is defined as the twisted version of the corresponding supersymmetric gauged WZW model. It is shown that this model is equivalent to a topological conformal field theory characterized by two independent topological conformal algebras, one of which is the "twisted Kazama-Suzuki type" and the other is "twisted Coulomb gas type". We further show that our formalism of this gauged WZW model naturally re...

It is shown that the asymmetric chiral gauging of the WZW models give rise to consistent string backgrounds. The target space structure of the ${[{SL(2,\Re)/ {SO(1,1)}}]}_L \bigotimes {[{SL(2,\Re)/U(1)}]}_R$ model is analyzed and the presence of a hidden isometry in this background is demonstrated. A nonlinear coordinate transformation is obtained which transforms the asymmetric model to the symmetric one, analyzed recently by two of the present authors.

We start by giving a brief introduction to string theory with emphasis on the example of the bosonic string. In order to fully appreciate string theory it is necessary to study the dynamics of the surface that the string traces out when moving in space-time. This is described by what is known as conformal field theory, which is the subject of chapter two. After this digression we return to string theory to give some insight into how the results of the articles contained in th...

We present a derivation of the N=1 and N=2 superconformal coset constructions starting from a supersymmetric WZW model where a diagonal subgroup has been gauged. We work in the general framework of self-dual (not necessarily reductive) Lie algebras; but even in the reductive case these results are new. We show that the BRST cohomology of the gauged supersymmetric WZW model contains the N=1 (and if it exists also the N=2) coset generators. We also extend the BRST analysis to s...

We construct two-parameter families of integrable $\lambda$-deformations of two-dimensional field theories. These interpolate between a CFT (a WZW/gauged WZW model) and the non-Abelian T-dual of a principal chiral model on a group/symmetric coset space. In examples based on the $SU(2)$ WZW model and the $SU(2)/U(1)$ exact coset CFT, we show that these deformations are related to bi-Yang-Baxter generalisations of $\eta$-deformations via Poisson-Lie T-duality and analytic conti...