Anti-de Sitter-space/conformal-field-theory Casimir energy for rotating black holes

We show that, if one chooses the Einstein static universe as the metric on the conformal boundary of Kerr-anti-de Sitter spacetime, then the Casimir energy of the boundary conformal field theory can easily be determined. The result is independent of the rotation parameters, and the total boundary energy then straightforwardly obeys the first law of thermodynamics. Other choices for the metric on the conformal boundary will give different, more complicated, results. As an application, we calculate the Casimir energy for free self-dual tensor multiplets in six dimensions and compare it with that of the seven-dimensional supergravity dual. They differ by a factor of 5/4.