The Thermodynamic Potentials of Kerr-AdS Black Holes and their CFT Duals

TL;DR

This paper compares thermodynamic potentials of Kerr-AdS black holes with their dual conformal field theories, analyzing weak and strong coupling regimes and revealing coupling-independent ratios and a unique logarithmic term at weak coupling.

Contribution

It provides the first detailed comparison of thermodynamic potentials between supergravity and dual field theories for rotating black holes, including subleading corrections.

Findings

Ratios of thermodynamic terms are coupling-independent for N=4 SYM.

A subleading logarithmic term appears in the M2 brane field theory but not in supergravity.

Leading and subleading terms match at one loop in field theory and supergravity.

Abstract

String or M-theory in the background of Kerr-AdS black holes is thought to be dual to the large n limit of certain conformal field theories on a rotating sphere at finite temperature. The five dimensional black hole is associated to N=4 supersymmetric Yang-Mills theory on a rotating three-sphere and the four dimensional one to the superconformal field theory of coinciding M2 branes on a rotating two-sphere. The thermodynamic potentials can be expanded in inverse powers of the radius of the sphere. We compute the leading and subleading terms of this expansion in the field theory at one loop and compare them to the corresponding supergravity expressions. The ratios between these terms at weak and strong coupling turns out not to depend on the rotation parameters in the case of N=4 SYM. For the field theory living on one M2 brane we find a subleading logarithmic term. No such term arises from the supergravity calculation.