Linearized Form of the Generic Affine-Virasoro Action

TL;DR

This paper introduces auxiliary fields to linearize the highly non-linear generic affine-Virasoro action, revealing its structure as a Diff S$_2$-gauged WZW model and clarifying its symmetry properties.

Contribution

The paper provides a linearized form of the generic affine-Virasoro action, making its Diff S$_2$-gauged WZW structure explicit and easier to analyze.

Findings

The linearized action explicitly shows the Diff S$_2$-gauged WZW structure.

Auxiliary fields transform as local Lie g × Lie g connections.

The reformulation simplifies understanding the symmetry properties.

Abstract

Halpern and Yamron have given a Lorentz, conformal, and Diff S$_2$-invariant world-sheet action for the generic irrational conformal field theory, but the action is highly non-linear. In this paper, we introduce auxiliary fields to find an equivalent linearized form of the action, which shows in a very clear way that the generic affine-Virasoro action is a Diff S$_2$-gauged WZW model. In particular, the auxiliary fields transform under Diff S$_2$ as local Lie $g$ $\times$ Lie $g$ connections, so that the linearized affine-Virasoro action bears an intriguing resemblance to the usual (Lie algebra) gauged WZW model.