Higher Spin Gravity and Exact Holography

TL;DR

This paper provides evidence for the Higher Spin/Vector Model correspondence through two examples: a constructive 4D higher spin theory from 3D models and an AdS_3/CFT_2 duality involving higher spin black holes, with results matching between gravity and CFT.

Contribution

It introduces a bi-local formulation for constructing higher spin theories from vector models and demonstrates the matching of black hole partition functions in higher spin gravity and CFT.

Findings

Bi-local fields describe bulk higher spin theories with interactions.

Partition functions of higher spin black holes match between gravity and CFT.

Evidence supports the Higher Spin/Vector Model duality.

Abstract

In this talk, we present some direct evidences of the Higher Spin/Vector Model correspondence. There are two particular examples we would like to address on. The first example concerns a constructive approach of four dimensional higher spin theory from 3d O(N) vector model based on a bi-local formulation. These bi-local fields are seen to give a bulk description of the higher spin theory with extra dimension and interactions. The second example is a similar AdS_3/CFT_2 duality put forward by Gaberdiel and Gopakumar. Specifically, we are interested in black hole solutions carrying nonzero higher spin charges. The partition function of the general hs[\lambda] higher spin black hole is computed from the CFT side using the W_\infty[\lambda] symmetry and we found a perfect agreement with the gravity result.