Asymptotic W-symmetries in three-dimensional higher-spin gauge theories

TL;DR

This paper systematically computes the asymptotic symmetry algebras of three-dimensional higher-spin gauge theories, deriving explicit formulas for W-algebras and exploring their structure and relation to known bases.

Contribution

It provides a closed-form formula for the structure constants of classical W_N algebras and extends the analysis to a family of higher-spin theories as large N limits.

Findings

Derived explicit structure constants for W_N algebras.

Established a relation between primary and non-primary bases.

Applied techniques to a family of higher-spin gauge theories.

Abstract

We discuss how to systematically compute the asymptotic symmetry algebras of generic three-dimensional bosonic higher-spin gauge theories in backgrounds that are asymptotically AdS. We apply these techniques to a one-parameter family of higher-spin gauge theories that can be considered as large N limits of SL(N) x SL(N) Chern-Simons theories, and we provide a closed formula for the structure constants of the resulting infinite-dimensional non-linear W-algebras. Along the way we provide a closed formula for the structure constants of all classical W_N algebras. In both examples the higher-spin generators of the W-algebras are Virasoro primaries. We eventually discuss how to relate our basis to a non-primary quadratic basis that was previously discussed in literature.