D1-D5 black hole microstate counting from supergravity

TL;DR

This paper quantizes the moduli space of D1-D5 microstates in Type IIB supergravity, revealing their structure as chiral bosons and confirming previous conjectures about their quantum properties.

Contribution

It introduces a novel covariant quantization approach for D1-D5 microstates directly from supergravity, confirming the effective Planck constant and the chiral boson nature of the moduli.

Findings

Components of the moduli space satisfy chiral boson commutation relations

The effective Planck constant matches previous U-duality conjectures

Quantization reduces to perturbations around plane wave geometries

Abstract

We quantize the moduli space of regular D1-D5 microstates, directly from Type IIB SUGRA. The moduli space is parametrized by a smooth closed non-selfintersecting curve in four dimensions, and we derive that the components of the curve satisfy chiral boson commutation relations, with the correct value of the effective Planck constant previously conjectured using U-duality. We use the Crnkovic-Witten-Zuckerman covariant quantization method, previously used to quantize the `bubbling AdS' geometries, combined with a certain new `consistency condition' which allows us to reduce the computation to quantizing perturbations around the plane wave.