Towards non-AdS holography in 3-dimensional higher spin gravity

TL;DR

This work advances non-AdS holography in three-dimensional higher spin gravity by formulating a generalized variational principle that remains well-posed for backgrounds beyond AdS. It shows, through explicit spin-4 constructions, how AdS, AdS$_2 imes ext{R}$, Schrödinger, Lifshitz, and warped AdS geometries can arise by selecting appropriate $sl(2)$ embeddings and higher-spin generators, with the principal embedding favoring Schrödinger/Lifshitz while non-principal embeddings enable warped AdS and AdS$_2 imes ext{R}$. The authors provide concrete Lifshitz black hole solutions and map out which backgrounds are accessible in each embedding, laying groundwork for dualities with non-relativistic or anisotropic 2D field theories. They outline a program to determine canonical charges, asymptotic symmetries, and holographic observables, aiming to extend gauge/gravity duality beyond AdS in a controlled, higher-spin context. Overall, the paper establishes higher spin gravity in 3D as a versatile platform for non-AdS holography and diverse gravity duals to 2D QFTs.

Abstract

We take the first steps towards non-AdS holography in higher spin gravity. Namely, we propose a variational principle for generic 3-dimensional higher spin gravity that accommodates asymptotic backgrounds beyond AdS, like asymptotically Schrodinger, Lifshitz or warped AdS spacetimes. As examples we study in some detail the four sl(2) embeddings of spin-4 gravity and provide associated geometries, including an asymptotic Lifshitz black hole.