On a `universal' class of WZW-type conformal models

TL;DR

This paper introduces a broad class of sigma models generalizing gauged WZW models, derives conditions for their conformal invariance at one loop, and demonstrates their exact invariance for various configurations, expanding understanding of conformal field theories.

Contribution

It formulates a universal algebraic condition for conformal invariance in generalized WZW-type models, encompassing known models and new classes with arbitrary target space couplings.

Findings

Derived algebraic equations for conformal invariance at one loop.

Explicitly demonstrated invariance for models associated with arbitrary G/H gauged theories.

Connected the invariance condition to the affine-Virasoro master equation.

Abstract

We consider a class of sigma models that appears from a generalisation of the gauged WZW model parametrised by a constant matrix $Q$. Particular values of $Q$ correspond to the standard gauged WZW models, chiral gauged WZW models and a bosonised version of the non-abelian Thirring model. The condition of conformal invariance of the models (to one loop or $1/k$-order but exactly in $Q$) is derived and is represented as an algebraic equation on $Q$. Solving this equation we demonstrate explicitly the conformal invariance of the sigma models associated with arbitrary $G/H$ gauged and chiral gauged WZW theories as well as of the models that can be represented as WZW model perturbed by integrably marginal operators (constructed from currents of the Cartan subalgebra $H_c$ of $G$). The latter models can be also interpreted as $G x H/H$ gauged WZW models and have the corresponding target space couplings (metric, antisymmetric tensor and dilaton) depending on an arbitrary constant matrix which parametrises an embedding of the abelian subgroup $H$ (isomorphic to $H_c$) into $G x H$. We discuss the relation of our conformal invariance equation to the large $k$ form of the master equation of the affine-Virasoro construction. Our equation describes `reducible' versions of some `irreducible' solutions (cosets) of the master equation. We suggest a classically non-Lorentz-invariant sigma model that may correspond to other solutions of the master equation.