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

TL;DR

Awad and Johnson extend the AdS/CFT correspondence to higher-dimensional Kerr-AdS black holes using holographic renormalization via counterterms to compute finite stress-energy tensors and actions. They compare gravity results with dual field theories on rotating Einstein universe backgrounds, finding exact zero-mass matches for Kerr-AdS5 and a universal high-temperature relation up to a 3/4 factor between strong- and weak-coupling stress tensors, along with a 4/7 anomaly mismatch in Kerr-AdS7 due to six-dimensional dynamics. They also present Kerr-AdS6 and Kerr-AdS7 results and discuss conformal anomalies in the dual theories, highlighting how rotation affects conformal versus scale invariance. Overall, the work supports the robustness of holographic renormalization and exposes dimension-dependent nuances in the AdS/CFT correspondence for rotating spacetimes.

Abstract

Using the counterterm subtraction technique we calculatehe stress-energy tensor, action, and other physical quantities for Kerr-AdS black holes in various dimensions. For Kerr-AdS_5 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 generalKerr-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 Kerr-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 Kerr-AdS_6, and Kerr-AdS_7 black holes, with one rotation parameter, and we display the results. We discuss the conformal anomalies of the field theories dual to the Kerr-AdS_5 and Kerr-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 non-trivial field theory. For Kerr-AdS_7 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-AdS_7 black hole (with zero mass parameter), up to that factor.