Higher spin gravity in three dimensions has explicit black holes solutions, carrying higher spin charge. We compute the free energy of a charged black hole from the holographic dual, a 2d CFT with extended conformal symmetry, and find exact agreement with the bulk thermodynamics. In the CFT, higher spin corrections to the free energy can be calculated at high temperature from correlation functions of W-algebra currents.

We use a Pohlmeyer type reduction to generate classical string solutions in AdS spacetime. In this framework we describe a correspondence between spikes in AdS 3 and soliton profiles of the sinh-Gordon equation. The null cusp string solution and its closed spinning string counterpart are related to the sinh-Gordon vacuum. We construct classical string solutions corresponding to sinh-Gordon solitons, antisolitons and breathers by the inverse scattering technique. The breather solutions can also be reproduced by the sigma model dressing method.

We pursue the construction of higher-spin theory in AdS4 from CFT3 of the O(N) vector model in terms of canonical collective fields. In null-plane quantization an exact map is established between the two spaces. The coordinates of the AdS4 space-time are generated from the collective coordinates of the bi-local field. This, in the light-cone gauge, provides an exact one-to-one reconstruction of bulk AdS4 space-time and higher-spin fields.

In a class of 2D CFTs with higher spin symmetry, we compute thermal twopoint functions of certain scalar primary operators in the presence of nonzero chemical potential for higher spin charge. These are shown to agree with the same quantity calculated holographically using scalar fields propagating in a charged black hole background of 3D higher spin gravity. This match serves as further evidence for the duality between W N minimal models at large central charge and 3D higher spin gravity. It also supports a recent prescription for computing boundary correlators of 'multi-trace' scalar primary operators in higher spin theories.