Consistent string backgrounds and completely integrable 2D field theories

TL;DR

This paper explores consistent string backgrounds via the $eta$-function equations, focusing on WZW models perturbed by integrable tachyon operators, revealing a rich algebraic structure and two formulations of the resulting theories.

Contribution

It applies the $eta$-function formalism to WZW models with integrable perturbations, uncovering a non-linear chiral algebra and two formulations of the non-abelian Toda theories.

Findings

Identification of a large non-linear chiral algebra extending Virasoro

Demonstration that only the non-reduced theory satisfies $eta$-function equations

Establishment of two formulations of the perturbed WZW models

Abstract

After reviewing the $\beta$-function equations for consistent string backgrounds in the $\sigma$-model approach, including metric and antisymmetric tensor, dilaton and tachyon potential, we apply this formalism to WZW models. We particularly emphasize the case where the WZW model is perturbed by an integrable marginal tachyon potential operator leading to the non-abelian Toda theories. Already in the simplest such theory, there is a large non-linear and non-local chiral algebra that extends the Virasoro algebra. This theory is shown to have two formulations, one being a classical reduction of the other. Only the non-reduced theory is shown to satisfy the $\beta$-function equations.