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 $\mathrm{Kerr}-{\mathrm{AdS}}_5$ 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 $\mathrm{Kerr}-{\mathrm{AdS}}_5$ black hole at zero mass parameter exactly matches the Casimir energy of the dual field theory. We show that at high temperature the general $\mathrm{Kerr}-{\mathrm{AdS}}_5$ 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 $\mathrm{Kerr}-{\mathrm{AdS}}_6$ and $\mathrm{Kerr}-{\mathrm{AdS}}_7$ black holes, with one rotation parameter, and we display the results. We discuss the conformal anomalies of the dual field theories to the $\mathrm{Kerr}-{\mathrm{AdS}}_5$ and $\mathrm{Kerr}-{\mathrm{AdS}}_7$ spacetimes. In these two field theories, we show that the rotation parameters break conformal invariance but not scale invariance, a novel result for a nontrivial field theory. For $\mathrm{Kerr}-{\mathrm{AdS}}_7$ black holes the conformal anomalies calculated on the gravity side and the dual (0,2) tensor multiplet theory are equal up to a factor of $4/7\times {4N}^3.$ We expect that the Casimir energy of the free field theory is the same as the energy of the $\mathrm{Kerr}-{\mathrm{AdS}}_7$ black hole (with zero mass parameter), up to that factor.

• Received 7 September 2000

DOI:https://doi.org/10.1103/PhysRevD.63.124023