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

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.