Black hole entropy in massive Type IIA

TL;DR

The paper demonstrates that the entropy of static dyonic BPS black holes in $AdS_4$ with hypermultiplets, realized in massive Type IIA on $AdS_4\times S^6$, can be microscopically reproduced by counting ground states in the dual 3d field theory using a topologically twisted index. By formulating the gravity entropy as an extremization problem with attractor constraints and computing the large-$N$ limit of the field theory index via localization and Bethe Ansatz techniques, the authors show a precise match at leading order between the Bekenstein-Hawking entropy and the microscopic degeneracy. The matching relies on a dictionary between charges and chemical potentials, and on identifying the same extremization structure in both pictures, including the relation between the horizon data and flavor fluxes. These results extend previous holographic entropy matches to theories with hypermultiplets and demonstrate robustness of the microscopic counting framework for AdS$_4$ black holes in massive IIA, with implications for the role of hypermultiplets in holographic entropy counting.

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.

Figures (1)

• Figure 1: Quiver diagram and superpotential of the 3d dual to massive Type IIA on $S^6$.