Non-AdS holography in 3-dimensional higher spin gravity - General recipe and example

TL;DR

This paper develops a general method to determine asymptotic symmetry algebras in non-AdS higher spin gravity and applies it to a specific spin-3 example, revealing the structure of the symmetry algebra and conditions for unitarity.

Contribution

It provides a general algorithm for classical and quantum asymptotic symmetry analysis in non-AdS higher spin gravity, demonstrated through a detailed spin-3 case study.

Findings

Asymptotic symmetry algebra includes quantum W_3^2 and u(1) algebras.

Unitary representations only exist at central charges c=0 and c=1.

The specific example exhibits a Lobachevsky boundary condition structure.

Abstract

We present the general algorithm to establish the classical and quantum asymptotic symmetry algebra for non-AdS higher spin gravity and implement it for the specific example of spin-3 gravity in the non-principal embedding with Lobachevsky (H^2xR) boundary conditions. The asymptotic symmetry algebra for this example consists of a quantum W_3^2 (Polyakov-Bershadsky) and an affine u(1) algebra. We show that unitary representations of the quantum W_3^2 algebra exist only for two values of its central charge, the trivial c=0 "theory" and the simple c=1 theory.