Topologically charged BPS microstates in AdS$_3$/CFT$_2$

TL;DR

This paper develops modified helicity-trace indices to count microstates of supersymmetric black holes in AdS3/CFT2, resolving previous mismatches and matching known results in different supersymmetry settings.

Contribution

It introduces new index techniques to account for momentum and winding sectors in AdS3/CFT2, enabling accurate microstate counting and resolving prior discrepancies.

Findings

Successfully reproduces microstate matching in $ abla$N=(4,4) case.

Resolves mismatch in Bekenstein-Hawking entropy for $ abla$N=(2,2) case.

Defines modified helicity-trace indices for momentum and winding sectors.

Abstract

In the standard $\mathcal{N}=(4,4)$ AdS$_3$/CFT$_2$ with $\mathrm{sym}^N(T^4)$, as well as the $\mathcal{N}=(2,2)$ Datta-Eberhardt-Gaberdiel variant with $\mathrm{sym}^N(T^4/\mathbb{Z}_2)$, supersymmetric index techniques have not been applied so far to the CFT states with target-space momentum or winding. We clarify that the difficulty lies in a central extension of the SUSY algebra in the momentum and winding sectors, analogous to the central extension on the Coulomb branch of 4d $\mathcal{N}=2$ gauge theories. We define modified helicity-trace indices tailored to the momentum and winding sectors, and use them for microstate counting of the corresponding bulk black holes. In the $\mathcal{N}=(4,4)$ case we reproduce the microstate matching of Larsen and Martinec. In the $\mathcal{N}=(2,2)$ case we resolve a previous mismatch with the Bekenstein-Hawking formula encountered in the topologically trivial sector by going to certain winding sectors.