Holography and Rotating AdS Black Holes

TL;DR

The paper tests the AdS/CFT correspondence by comparing the thermodynamics of a rotating Kerr–AdS black hole in five dimensions with a dual four-dimensional conformal field theory on S^3. It first confirms holography for the nonrotating case and then extends to rotation, showing that in the high-temperature limit the entropy, energy, and angular momentum match between gravity and the boundary CFT up to a universal factor of 4/3, independent of the rotation. The discrepancy is attributed to using the free-field limit on the gauge theory side rather than the strongly coupled regime required by the correspondence. Together, these results reinforce the robustness of holography for rotating AdS black holes and illuminate how coupling effects may alter gauge theory thermodynamics while preserving core holographic relations.

Abstract

We probe the AdS/CFT correspondence by comparing the thermodynamics of a rotating black hole in five-dimensional anti-de Sitter space with that of a conformal field theory on $S^3$, whose parameters come from the boundary of spacetime. In the high temperature limit, we find agreement between gauge theory and gravity in all thermodynamic quantities upto the same factor of 4/3 that appears for nonrotating holes.