The Kerr/CFT correspondence and string 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 ${\mathrm{AdS}}_{2}$ structure. To understand the dual chiral ${\mathrm{CFT}}_{2}$, 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 Breckenridge-Myers-Peet-Vafa black holes, and obtain the correct entropies for the black holes microscopically. These have an ${\mathrm{AdS}}_{3}$ structure in the near horizon geometry and an ${\mathrm{AdS}}_{2}$ structure in the very near horizon geometry. We identified one of the two Virasoro symmetries in the nonchiral ${\mathrm{CFT}}_{2}$ dual to the ${\mathrm{AdS}}_{3}$, i.e., in the ${\mathrm{AdS}}_{3}/{\mathrm{CFT}}_{2}$, with the Virasoro symmetry in the chiral ${\mathrm{CFT}}_{2}$ dual to the ${\mathrm{AdS}}_{2}$, i.e., in the Kerr/CFT correspondence. We also discuss a way to understand the chiral ${\mathrm{CFT}}_{2}$ 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.