Real-time Correlators and Hidden Conformal Symmetry in Kerr/CFT Correspondence

TL;DR

This paper demonstrates that hidden conformal symmetry in Kerr and Kerr-Newman black holes allows for the calculation of real-time correlators that match two-dimensional CFT predictions, supporting the Kerr/CFT correspondence.

Contribution

It reveals hidden conformal symmetry in Kerr-Newman black holes and computes correlators that align with CFT, extending Kerr/CFT correspondence to charged and higher-spin fields.

Findings

Real-time correlators match CFT predictions for scalar scattering.

Hidden conformal symmetry exists in Kerr-Newman black holes.

Green's functions for photons and gravitons agree with CFT expectations.

Abstract

In this paper, we study the real-time correlators in Kerr/CFT, in the low frequency limit of generic non-extremal Kerr(-Newman) black holes. From the low frequency scattering of Kerr-Newman black holes, we show that for the uncharged scalar scattering, there exists hidden conformal symmetry on the solution space. Similar to Kerr case, this suggests that the Kerr-Newman black hole is dual to a two-dimensional CFT with central charges $c_L=c_R=12J$ and temperatures $T_L=\frac{(r_++r_-)-Q^2/M}{4\pi a}, T_R=\frac{r_+-r_-}{4\pi a}$. Using the Minkowski prescription, we compute the real-time correlators of charged scalar and find perfect match with CFT prediction. We further discuss the low-frequency scattering of photons and gravitons by Kerr black hole and find that their retarded Green's functions are in good agreement with CFT prediction. Our study supports the idea that the hidden conformal symmetry in the solution space is essential to Kerr/CFT correspondence.