Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields

TL;DR

This paper explores how W-algebras emerge as asymptotic symmetries in three-dimensional higher-spin gravity theories, specifically analyzing models with spin-3 fields coupled to Einstein gravity with a negative cosmological constant.

Contribution

It demonstrates that the asymptotic symmetry algebra of these higher-spin models is given by two copies of the classical W_3-algebra, extending the Brown-Henneaux results to higher-spin contexts.

Findings

Asymptotic symmetry algebra is W_3 for spin-3 coupled gravity.

The central charge matches the Brown-Henneaux value.

The analysis applies to finite higher-spin field models.

Abstract

We discuss the emergence of W-algebras as asymptotic symmetries of higher-spin gauge theories coupled to three-dimensional Einstein gravity with a negative cosmological constant. We focus on models involving a finite number of bosonic higher-spin fields, and especially on the example provided by the coupling of a spin-3 field to gravity. It is described by a SL(3) \times SL(3) Chern-Simons theory and its asymptotic symmetry algebra is given by two copies of the classical W_3-algebra with central charge the one computed by Brown and Henneaux in pure gravity with negative cosmological constant.