AdS/CFT Casimir Energy for Rotating Black Holes

TL;DR

This paper calculates the Casimir energy of boundary conformal field theories in AdS/CFT correspondence for rotating black holes, showing independence from rotation parameters and consistency with thermodynamics, with applications to six-dimensional tensor multiplets.

Contribution

It provides a straightforward method to determine Casimir energy in Kerr-AdS spacetimes using the Einstein Static Universe boundary metric, highlighting metric choice effects.

Findings

Casimir energy is independent of rotation parameters.

Boundary energy obeys the first law of thermodynamics.

Comparison between free tensor multiplets and supergravity duals shows a factor of 5/4 difference.

Abstract

We show that if one chooses the Einstein Static Universe as the metric on the conformal boundary of Kerr-AdS 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.