Counting D1-D5-P Microstates in Supergravity

TL;DR

This paper quantizes D1-D5-P superstrata microstate geometries in supergravity, confirming the counting of microstates and their growth rate, which is smaller than that of the black hole, using a novel symplectic form approach.

Contribution

It introduces a direct supergravity quantization method for superstrata microstates, fixing the symplectic form uniquely via Rychkov's condition and confirming results with explicit calculations.

Findings

Quantization of superstrata microstates in supergravity.

Agreement with previous microstate counts.

Microstate growth is parametrically smaller than black hole entropy.

Abstract

We quantize the D1-D5-P microstate geometries known as superstrata directly in supergravity. We use Rychkov's consistency condition [hep-th/0512053] which was derived for the D1-D5 system; for superstrata, this condition turns out to be strong enough to fix the symplectic form uniquely. For the $(1,0,n)$ superstrata, we further confirm this quantization by a bona-fide explicit computation of the symplectic form using the semi-classical covariant quantization method in supergravity. We use the resulting quantizations to count the known supergravity superstrata states, finding agreement with previous countings that the number of these states grows parametrically smaller than those of the corresponding black hole.