The Kerr/CFT Correspondence and String Theory

TL;DR

This work investigates the origin of the Kerr/CFT correspondence by embedding extremal black holes in string theory through rotating D1-D5-P systems, which admit both an AdS$_3$ throat and a very near horizon AdS$_2$-fibered geometry. Using Brown–Henneaux techniques, it computes the central charges in the AdS$_3$ region as $c^L=c^R=6N_1N_5$, and, in the very near horizon limit, identifies three ASGs each capable of enhancing to a Virasoro algebra with central charges $c^y=6N_1N_5$, $c^{\phi}=12N_\psi$, and $c^{\psi}=12N_\phi$, corresponding to distinct chiral CFT$_2$ sectors. The temperatures for these sectors yield a consistent microscopic entropy via the Cardy formula: $S_{micro}=\frac{\pi^2}{3}c T = 2\pi\sqrt{N_1N_5N_p+\frac{N_\phi N_\psi}{4}}$, matching the Bekenstein–Hawking entropy for extremal D1-D5-P black holes. The analysis supports interpreting Kerr/CFT as a decoupling limit focusing on ground states with fixed charges, while highlighting a universal aspect of very near horizon geometries and suggesting that the chiral CFT$_2$ emerges from a high-energy completion of the AdS$_3$/CFT$_2$ dual theory.

Abstract

The Kerr/CFT correspondence is a holographic duality between a two dimensional chiral conformal field theory (CFT) and the very near horizon limit of an extremal black hole, which includes an AdS2 structure. To understand the dual chiral CFT2, we apply the Kerr/CFT correspondence to a certain class of black holes embedded in string theory, which include the D1-D5-P and the BMPV black holes, and obtain the correct entropies for the black holes microscopically. These have an AdS3 structure in the near horizon geometry and an AdS2 structure in the very near horizon geometry. We identified one of the two Virasoro symmetries in the nonchiral CFT2 dual to the AdS3, i.e. in the AdS3/CFT2, with the Virasoro symmetry in the chiral CFT2 dual to the AdS2, i.e. in the Kerr/CFT correspondence. We also discuss a way to understand the chiral CFT2 dual to generic extremal black holes. A kind of universality for the very near horizon geometries of extremal black holes will be important for the validity of the Kerr/CFT correspondence. Based on this analysis, we propose that the Kerr/CFT correspondence can be understood as a decoupling limit in which only the ground states remain.