Holography Beyond AdS/CFT: Explorations in Kerr/CFT and Higher Spin DS/CFT

Abstract

In this thesis we explore holography beyond the much studied case of AdS/CFT by considering two less well understood dualities: the Kerr/CFT and dS/CFT conjectures. Conformal symmetry continues to appear as a central organizing principle in both cases. In the first part of the thesis we use Kerr/CFT to shed light on the microscopic origin of black hole entropy. Specifically we consider corrections, logarithmic in the horizon area, to the microcanonical entropy of spinning black holes in dimensions four and greater. The logarithmic corrections to the black hole area/entropy law are entirely determined macroscopically by the massless particle spectrum, and therefore serve as powerful consistency checks on any proposed enumeration of black hole microstates. We compute these corrections microscopically using the Kerr/CFT correspondence and provide support for the conjecture by successfully matching the macroscopic computation in the simpler case of odd dimensions. The match depends sensitively on the values of the CFT central charge and the levels of the Kac Moody current algebras corresponding to spacetime and gauge isometries and sheds light on the statistical ensembles occurring in Kerr/CFT. We also take the extremal limit of the non-extremal microscopic computation and reproduce the macroscopic logarithmic corrections to the extremal black hole. In the second part of the thesis we discuss the simplest known explicit examples of dS$_4$/CFT$_3$: the duality between Vasiliev's higher spin gravity in dS$_4$ and three dimensional Euclidean vector model CFT's. In particular we conjecture that the level $k$ $U(N)$ Chern-Simons theory coupled to free anticommuting scalar matter in the fundamental is dual to non-minimal higher-spin Vasiliev gravity in dS$_4$ with parity-violating phase $\theta_0={\pi N\over 2k}$ and Neumann boundary conditions for the scalar. Related conjectures are made for fundamental commuting spinor matter and critical theories. This generalizes a recent conjecture relating the minimal Type A Vasiliev theory in dS$_4$ to the $Sp(N)$ model with fundamental real anti-commuting scalars.