Sigma model of near-extreme rotating black holes and their microstates

TL;DR

This paper models near-extreme rotating black holes in five dimensions using a conformal sigma model, linking their microstates to string oscillations and accurately reproducing their entropy.

Contribution

It introduces a sigma model description for rotating black holes with large brane charges, connecting black hole microstates to string theory in a novel way.

Findings

The sigma model is a marginal deformation of a WZW model with levels equal to the brane charge.

The microstates correspond to string oscillations in transverse directions.

The statistical entropy matches the Bekenstein-Hawking entropy.

Abstract

Five-dimensional non-extreme rotating black holes with large NS-NS five-brane and fundamental string charge are shown to be described by a conformal sigma model, which is a marginal integrable deformation of six-dimensional SL(2,R) x SU(2) WZW model. The two WZW levels are equal to the five-brane charge, while the parameters of the two marginal deformations generated by the left and right chiral SU(2) currents are proportional to the two angular momentum components of the black hole. The near-horizon description is effectively in terms of a free fundamental string whose tension is rescaled by the five-brane charge. The microstates are identified with those of left and right moving superconformal string oscillations in the four directions transverse to the five-brane. Their statistical entropy reproduces precisely the Bekenstein-Hawking entropy of the rotating black hole.