Hidden conformal symmetry of extremal Kaluza-Klein black hole in four dimensions

TL;DR

This paper reveals a hidden conformal symmetry in extremal Kaluza-Klein black holes, connecting their near-region scalar dynamics to conformal field theory, and matching thermodynamic and correlator predictions.

Contribution

It demonstrates the presence of hidden conformal symmetry in extremal Kaluza-Klein black holes and derives dual CFT charges using thermodynamics.

Findings

Scalar Laplacian matches $SL(2,)$ Casimir

Real-time correlators agree with CFT predictions

Conjugate charges derived from thermodynamics

Abstract

We study the hidden conformal symmetry of four-dimensional extremal Kaluza-Klein black hole. The scalar Laplacian corresponding to the radial equation in the near-region is rewritten in terms of the $SL(2,\mathbb R)$ quadratic Casimir. Using the first law of black hole thermodynamics, this symmetry enables us to obtain the conjugate charges for the CFT side. The real-time correlators are also found to agree with the CFT expectations.