Infinite-Dimensional Symmetries of Two-Dimensional Coset Models Coupled to Gravity

TL;DR

This paper explores the infinite-dimensional symmetries, including affine Kac-Moody and Virasoro algebras, of two-dimensional symmetric-space sigma models coupled to gravity, extending previous flat spacetime results to include gravitational interactions.

Contribution

It provides explicit constructions of symmetry transformations for 2D SSMs coupled to gravity, revealing the structure of affine Kac-Moody and Virasoro symmetries in this context.

Findings

Explicit expressions for affine Kac-Moody symmetry transformations.

Construction of Virasoro mode transformations with n ≥ -1.

Extension of symmetry analysis from flat to gravitationally coupled models.

Abstract

In an earlier paper we studied the infinite-dimensional symmetries of symmetric-space sigma models (SSMs) in a flat two-dimensional spacetime. Here, we extend our investigation to the case of two-dimensional SSMs coupled to gravity. These theories arise from the toroidal reduction of higher-dimensional gravity and supergravities to two dimensions. We construct explicit expressions for the symmetry transformations under the affine Kac-Moody extension $\hat G$ that arises when starting from a G/H coset model. We also construct further explicit symmetry transformations that correspond to the modes L_n of a Virasoro subalgebra with $n\ge -1$.