We investigate higher spin theories of gravity in three dimensions based on the gauge group SL(N, R) × SL(N, R). In these theories the usual diffeomorphism symmetry is enhanced to include higher spin gauge transformations under which traditional geometric notions of curvature and causality are no longer invariant. This implies, for example, that apparently singular geometries can be rendered smooth by a gauge transformation, much like the resolution of orbifold singularities in string theory. The classical solutions, including the recently constructed higher spin black hole, are characterized by their holonomies around the non-contractible cycles of space-time. The black hole solutions are shown to be gauge equivalent to a BTZ black hole which is charged under a set of U (1) Chern-Simons fields. Nevertheless, depending on the choice of embedding of the gravitational gauge group, the space-time geometry may be nontrivial. We study in detail the N = 3 example, where this observation allows us to find a gauge where the black hole geometry takes a simple form and the thermodynamic properties can be studied. 1

The dS/CFT proposal of Anninos, Hartman, and Strominger relates quantum Vasiliev gravity in dS 4 to a large N vector theory in three dimensions. We use this proposal to compute the Wheeler-de Witt wave function of a universe having a particular topology at future infinity. This amplitude is found to grow rapidly with the topological complexity of the spatial slice; this is due to the plethora of states of the Chern-Simons theory that is needed to impose the singlet constraint. Various mechanisms are considered which might ameliorate this growth, but none seems completely satisfactory. We also study the topology dependence in Einstein gravity by computing the action of complex instantons; the wave function then depends on a choice of contour through the space of metrics. The most natural contour prescription leads to a growth with genus similar to the one found in Vasiliev theory, albeit with a different power of Newton's constant.

We study SL(N, R) Chern-Simons gauge theories in three dimensions. The choice of the embedding of SL(2, R) in SL(N, R), together with asymptotic boundary conditions, defines a theory of higher spin gravity. Each inequivalent embedding leads to a different asymptotic symmetry group, which we map to an OPE structure at the boundary. A simple inspection of these algebras indicates that only the W N algebra constructed using the principal embedding could admit a unitary representation for large values of the central charge.

We consider theories of three dimensional quantum gravity in Anti-de Sitter space which possess massless higher-spin gauge symmetry. The perturbative spectrum of the theory includes higher spin excitations which can be organized into vacuum representations of the W N algebra; these are higher spin versions of the boundary gravitons. We describe a fundamental bound which relates the value of the cosmological constant to the amount of gauge symmetry present. In the dual CFT language, this is the statement that modular invariance implies that the theory can not be quantized unless the central charge is sufficiently large, i.e. if c ≥ N − 1. This bound relies on the assumption that all of the perturbative excitations exist as full states in the quantum theory, and can be circumvented if the theory possesses a linearization instability. The W N minimal models -recently conjectured to be dual to certain higher spin AdS theories by Gaberdiel and Gopakumar -provide an example of this phenomenon. This result can be regarded as an example of a "gravitational exclusion principle" in Anti-de Sitter space, where a non-perturbative quantum gravity mechanism involving black holes places a limit on the number of light degrees of freedom present. 1

We consider CFTs conjectured to be dual to higher spin theories of gravity in AdS 3 and AdS 4 . Two dimensional CFTs with W N symmetry are considered in the λ = 0 (k → ∞) limit where they are conjectured to be described by continuous orbifolds. The torus partition function is computed, using reasonable assumptions, and equals that of a free field theory. We find no phase transition at temperatures of order one; the usual Hawking-Page phase transition is removed by the highly degenerate light states associated with conical defect states in the bulk. Three dimensional Chern-Simons Matter CFTs with vector-like matter are considered on T 3 , where the dynamics is described by an effective theory for the eigenvalues of the holonomies. Likewise, we find no evidence for a Hawking-Page phase transition at large level k.