Gauged WZW Model Research Articles

Cosmological string backgrounds from gauged WZW models

We discuss the four-dimensional target-space interpretation of bosonic strings based on gauge WZW models, in particular of those based on the non-compact coset space SL (2, R )×SO(1, 1). We show that these theories lead, apart from the recently broadly discussed black-hole type of backgrounds, to cosmological string backgrounds, such as an expanding Universe. Which of the two cases is realized depends on the sign of the level of the corresponding Kac-Moody algebra. We discuss various aspects of these new cosmological string backgrounds.

Extra observables in gauged WZW models

It is known that Liouville theory can be presented as an SL(2, R ) gauged WZW model. We study a two-dimensional field theory which can be obtained by analytically continuing some of the variables in the SL(2, R ) gauged WZW model. We can derive Liouville theory from the analytically continued model, (which is gauged SL(2, C /SU(2) model,) in a similar but more rigorous way than from the original gauged WZW model. We investigate the obsevables of this gauged SL(2, C )/SU(2) model. We find infinitely many extra observables which can not be identified with operators in Liouville theory. We concentrate on observables which are (1, 1) forms and the correlators of their integralsover two-dimensional spacetime. At a special value of the coupling constant of our model, the correlators of these integrals on the sphere coincide with the results from matrix models.

The N matrix model and gauged WZW models

It has been shown that the N matrix model two-dimensional gravity is related to certain topological field theories obtained by twisting the N = 2 minimal models. In this paper, the latter theories are studied by realizing them as gauged WZW models. This leads to an algebrogeometric description of the topological correlation functions from which many of their standard properties can be recovered. We find that in a certain sense the model at level k, with k analytically continued to −3, is equivalent to the Penner model (which computes the Euler characteristic of the moduli space of Riemann surfaces). We also gain better understanding of formulas of Lerche, Vafa, and Warner; Gepner; and Spiegelglas.

A superstring theory in four curved space-time dimensions

Neveu-Schwarz-Ramond type heterotic and type-II superstrings in 4D curved space-time are constructed as exact N = 1 superconformal theories. The tachyon is eliminated with a GSO projection. The theory is based on the N = 1 superconformal gauged WZW model for the anti-de Sitter coset SO(3, 2)/SO(3, 1) with integer central extension k=5. The model has dynamical duality properties in its space-time metric that are similar to the large-small ( R→1/ R) duality of tori. To first order in a 1/ k expansion we give expressions for the metric, the dilaton, the Ricci tensor and their dual generalizations. The curvature scalar has several singularities at various locations in the 4D manifold. This provides a new singular solution to Einstein's equations in the presence of matter in four dimensions. A non-trivial path integral measure which we conjectured in previous work for gauged WZW models is verified.

Black hole physics and Liouville theory

Hamiltonian path integral quantization of the SO(2, 1)/SO(2) and SO(2, 1)/SO(1, 1) gauged WZW models is considered. The SO(2, 1)/SO(2) model yields the Liouville theory coupled to a free scalar field theory after eliminating the group coordinates in favor of their conjugate momenta. The SO(2, 1)/SO(1, 1) model, recently argued to be a two-dimensional black-hole solution to string theory, can also be studied in momentum space. The resulting negative-metric Liouville-like theory has indefinite cosmological constant, is coupled to a positive-metric free scalar field, and lives on a Minkowski world sheet. The scaling variable |μ| of Liouville theory is related to the mass of the black hole. The connection to Liouville theory should provide the exact solution for correlation functions in the euclidean black-hole geometry using matrix models and Liouville theory; for the Lorentz-signature Schwarzschild geometry it gives us a tool to investigate the properties of singularities in string theory.

Classical W algebras and non-abelian parafermions

We show that the known classical W algebras can be derived from the algebra satisfied by the non-abelian parafermion fields of the gauged WZW model. The extension of this construction to multi-local fields leads to new W-algebras.

Gauged WZW models and the coset construction

Gauged WZW models and the coset construction

KdV type equations from gauged WZW models and conformal-like gauge of W-gravity

We show that the Wess-Zumino-Witten models provide Toda and KdV type integrable equations when they are properly constrained. This allows us to connect soliton theories with the Chern-Simons type gauge theories at the classical level. Toda field equations appear as zero curvature conditions which again are the classical equations of motion of the constrained WZW actions. Bäcklund transformations appear naturally as gauge transformations and explicit transformation rules for Toda and KdV type equations are derived. We also show that the conformal-like gauge of W-gravity is related to the generalization of the Toda field theory.

G/H conformal field theory from gauged WZW model

We show that the coset construction for affine algebras ĝ ⊃ ĥ can be realized by coupling a group G WZW model to a gauge field taking values in the Lie algebra h. The partition function of the coset models is computed exactly in terms of the branching functions of ĝ⊃ĥ. Correlation functions may be expressed in terms of those of the G-valued WZW model and of the H scc/H-valued one, also exactly soluble. The special cases include unitary, superconformal, paramefermionic and other discrete series.