Conformal weights in the Kerr/CFT correspondence

TL;DR

This paper extends the study of conformal weights in the Kerr/CFT correspondence to five-dimensional black holes, showing that operators dual to symmetric perturbations have universal integer conformal weights across various black hole types.

Contribution

It generalizes the analysis of conformal weights from four-dimensional Kerr black holes to a broad class of five-dimensional black holes with two rotational symmetries.

Findings

Operators dual to gravitational perturbations have integer conformal weights.

The conformal weights are consistent across different five-dimensional black holes.

Symmetry-preserving perturbations lead to universal conformal weights.

Abstract

It has been conjectured that a near-extreme Kerr black hole is described by a 2d CFT. Previous work has shown that CFT operators dual to axisymmetric gravitational perturbations have integer conformal weights. In this paper, we study the analogous problem in 5d. We consider the most general near-extreme vacuum black hole with two rotational symmetries. This includes Myers-Perry black holes, black rings and Kaluza-Klein black holes. We find that operators dual to gravitational (or electromagnetic or massless scalar field) perturbations preserving both rotational symmetries have integer conformal weights, the same for all black holes considered.