New Spin-Two Gauged Sigma Models and General Conformal Field Theory

TL;DR

This paper develops new conformal field theories via spin-two gauged sigma models, including gauged WZW and coset models, expanding the understanding of irrational CFTs with local gauge symmetries.

Contribution

It introduces the action formulation of new conformal field theories based on spin-two gauged sigma models, encompassing affine-Virasoro and g/h coset constructions.

Findings

Derived the action formulation for new conformal field theories.

Identified g/h coset models as local Lie h-invariant CFTs.

Connected the models to irrational conformal field theories with gauge symmetry.

Abstract

Recently, we have studied the general Virasoro construction at one loop in the background of the general non-linear sigma model. Here, we find the action formulation of these new conformal field theories when the background sigma model is itself conformal. In this case, the new conformal field theories are described by a large class of new spin-two gauged sigma models. As examples of the new actions, we discuss the spin-two gauged WZW actions, which describe the conformal field theories of the generic affine-Virasoro construction, and the spin-two gauged g/h coset constructions. We are able to identify the latter as the actions of the local Lie h-invariant conformal field theories, a large class of generically irrational conformal field theories with a local gauge symmetry.