Rotation and the AdS/CFT correspondence

TL;DR

The paper analyzes thermodynamics of rotating Kerr–AdS black holes across dimensions 3–5 and their dual conformal field theories on rotating Einstein universes. It shows that in the critical-velocity limit, where the boundary rotates at the speed of light, both bulk AdS–Kerr actions and boundary CFT partition functions exhibit divergent behavior with matching structure, supporting a holographic connection in these limits. By deriving explicit expressions for the BTZ, Kerr–AdS4, and AdS–Kerr5D solutions (including a new 5D case) and comparing to conformal field theory results, the work highlights how high-temperature/critical-velocity regimes reveal universal features of the AdS/CFT correspondence and potentially probe large-N Yang–Mills dynamics. The analysis also clarifies the role of reference backgrounds and vacuum energy, suggesting the correspondence may be most reliable in these limiting regimes and offering a framework for further tests in higher-dimensional holography.

Abstract

In asymptotically flat space a rotating black hole cannot be in thermodynamic equilibrium because the thermal radiation would have to be co-rotating faster than light far from the black hole. However in asymptotically anti-de Sitter space such equilibrium is possible for certain ranges of the parameters. We examine the relationship between conformal field theory in rotating Einstein universes of dimensions two to four and Kerr anti-de Sitter black holes in dimensions three to five. The five dimensional solution is new. We find similar divergences in the partition function of the conformal field theory and the action of the black hole at the critical angular velocity at which the Einstein rotates at the speed of light. This should be an interesting limit in which to study large $N$ Yang-Mills.

Figures (1)

• Figure 1: Plot of black hole radius $r_{+}$ against $al$. For $r_{+} < 1/l$, the action is positive, whilst the action blows up along the line $al = 1$. The lower line denotes the radius of the extreme black hole $r_{c}$ as a function of $a$. In the hatched region $r_{c}^2 \le r_{+}^2 < a/l$ the Einstein universe on the boundary rotates faster than the speed of light. The action is finite and positive at $r_{+}^2 = a/l$ but infinite and positive for extreme black holes. In three dimensions the supersymmetric limit coincides with $r_{+}^2 = a/l$, whilst in five and higher dimensions the cosmological bound is at $r_c = 0$.