Holographic microstate counting for AdS$_4$ black holes in massive IIA supergravity

TL;DR

This paper successfully derives the entropy of certain BPS black holes in massive IIA supergravity by counting supersymmetric states in a dual field theory, revealing the importance of the imaginary part of the partition function.

Contribution

It establishes a microscopic counting method for AdS$_4$ black hole entropy using the topologically twisted index in a dual 3D gauge theory, connecting it with the attractor mechanism.

Findings

Matching of microscopic index with Bekenstein-Hawking entropy

Demonstration of the role of the imaginary part of the partition function in holography

Validation of the $ ext{I}$-extremization principle in this context

Abstract

We derive the Bekenstein-Hawking entropy for a class of BPS black holes in the massive type IIA supergravity background AdS$_4 \times S^6$ from a microscopic counting of supersymmetric ground states in a holographically dual field theory. The counting is performed by evaluating the topologically twisted index of three-dimensional $\mathcal{N}=2$ Chern-Simons-matter gauge theories in the large $N$ limit. The $\mathcal{I}$-extremization principle is shown to match the attractor mechanism for the near-horizon geometries constructed in the four-dimensional dyonic $\mathcal{N}=2$ gauged supergravity, that arises as a consistent truncation of massive type IIA supergravity on $S^6$. In particular, our results prove that the imaginary part of the three-dimensional partition functions plays a crucial r\^ole in holography.