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

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 rôle in holography.

33 pages; v2: ref added, typos corrected; v3: published version

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• Signatures of the accelerating black holes with a cosmological constant from the ${\text{Sgr A}}^{\star }$ and ${\text{M87}}^{\star }$ shadow prospects
• Supersymmetric solutions from N=6 gauged supergravity
• Rotating black holes in the FI-gauged $N=2$, $D=4$ ${\overline{\mathbb{C}\text{P}}}^n$ model
• Uplifting dyonic AdS${}_4$ black holes on seven-dimensional Sasaki-Einstein manifolds
• The topologically twisted index of $\mathcal{N}=4$ SU($N$) Super-Yang-Mills theory and a black hole Farey tail