Higher Spin Gravity and Exact Holography

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.