Higher dimensional Kerr-AdS black holes and the AdS/CFT correspondence

Abstract

Using the counterterm subtraction technique we calculate the stress-energy tensor, action, and other physical quantities for Kerr-AdS black holes in various dimensions. For Kerr-AdS5 black holes with both rotation parameters nonzero, we demonstrate that the stress-energy tensor, in the zero mass parameter limit, is equal to the stress tensor of the weakly coupled four dimensional dual field theory. As a result, the total energy of the general Kerr-AdS5 black hole at zero mass parameter exactly matches the Casimir energy of the dual field theory. We show that at high temperature the general Kerr-AdS5 and perturbative field theory stress-energy tensors are equal, up to the usual factor of 3/4. We also use the counterterm technique to calculate the stress tensors and actions for Kerr-AdS6 and Kerr-AdS7 black holes, with one rotation parameter, and we display the results. We discuss the conformai anomalies of the dual field theories to the Kerr-AdS5 and Kerr-AdS7 spacetimes. In these two field theories, we show that the rotation parameters break conformai invariance but not scale invariance, a novel result for a nontrivial field theory. For Kerr-AdS7 black holes the conformai anomalies calculated on the gravity side and the dual (0,2) tensor multiplet theory are equal up to a factor of 4/7X4//3. We expect that the Casimir energy of the free field theory is the same as the energy of the Kerr-AdSy black hole (with zero mass parameter), up to that factor. ©2001 The American Physical Society.