Higher Dimensional Kerr–AdS Black Holes and the AdS/CFT Correspondence

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 with both rotation parameters non–zero, we demonstrate that 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 conformal anomalies of the field theories dual to the Kerr–AdS5 and Kerr– AdS7 spacetimes. In these two field theories, we show that the rotation parameters break conformal invariance but not scale invariance, a novel result for a non–trivial field theory. For Kerr–AdS7 the conformal anomalies calculated on the gravity side and the dual (0,2) tensor multiplet theory are equal up to 4/7 factor. We expect that the Casimir energy of the free field theory is the same as the energy of the Kerr–AdS7 black hole (with zero mass parameter), up to that factor.