Black hole entropy in massive Type IIA

TL;DR

This paper demonstrates that the entropy of certain BPS black holes in AdS4 can be exactly matched with microscopic state counting in the dual field theory using localization, confirming the AdS/CFT correspondence.

Contribution

It provides the first exact microscopic entropy calculation for BPS black holes in AdS4 in massive Type IIA supergravity using the topologically twisted index.

Findings

Exact match between black hole entropy and field theory index at leading order.

Application of localization techniques to compute the topologically twisted index.

Validation of the AdS/CFT correspondence for these black holes.

Abstract

We study the entropy of static dyonic BPS black holes in AdS$_4$ in 4d $\mathcal{N}=2$ gauged supergravities with vector and hyper multiplets, and how the entropy can be reproduced with a microscopic counting of states in the AdS/CFT dual field theory. We focus on the particular example of BPS black holes in AdS$_4 \times S^6$ in massive Type IIA, whose dual three-dimensional boundary description is known and simple. To count the states in field theory we employ a supersymmetric topologically twisted index, which can be computed exactly with localization techniques. We find perfect match at leading order.