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

Seyed Morteza Hosseini, Kiril Hristov, Achilleas Passias

TL;DR

This work provides a microscopic holographic account of BPS AdS$_4$ black hole entropy in massive IIA by computing the topologically twisted index of the dual 3d ${\cal N}=2$ CS-matter theories at large $N$ and implementing $\mathcal{I}$-extremization. The authors establish a precise link between the field-theory extremum and the four-dimensional attractor mechanism in the dyonic STU model, including the crucial role of the imaginary part of the partition function. They explicitly analyze the D2$_k$ theory and its AdS$_4\times S^6$ dual, deriving analytic UV and IR geometries and validating the entropy match $\mathcal{I}|_{\rm crit}=S_{\rm BH}$. The results extend the holographic entropy program to a massive IIA setting and illustrate a deep correspondence between horizon data and extremized field-theory indices.

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.

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

TL;DR

This work provides a microscopic holographic account of BPS AdS black hole entropy in massive IIA by computing the topologically twisted index of the dual 3d CS-matter theories at large and implementing -extremization. The authors establish a precise link between the field-theory extremum and the four-dimensional attractor mechanism in the dyonic STU model, including the crucial role of the imaginary part of the partition function. They explicitly analyze the D2 theory and its AdS dual, deriving analytic UV and IR geometries and validating the entropy match . The results extend the holographic entropy program to a massive IIA setting and illustrate a deep correspondence between horizon data and extremized field-theory indices.

Abstract

We derive the Bekenstein-Hawking entropy for a class of BPS black holes in the massive type IIA supergravity background AdS 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 Chern-Simons-matter gauge theories in the large limit. The -extremization principle is shown to match the attractor mechanism for the near-horizon geometries constructed in the four-dimensional dyonic gauged supergravity, that arises as a consistent truncation of massive type IIA supergravity on . In particular, our results prove that the imaginary part of the three-dimensional partition functions plays a crucial rôle in holography.

Paper Structure

This paper contains 20 sections, 123 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The topologically twisted index
  3. The large $\bm{N}$ limit of the index for a generic theory
  4. The index of D2$_{\bm k}$ at large ${\bm N}$
  5. AdS$_{\bm 4}$ black holes in $\bm{\mathcal{N}=2}$ dyonic STU gauged supergravity
  6. Black hole ansatz and BPS conditions
  7. Constant scalars, analytic UV and IR geometries
  8. Asymptotic AdS$_4$ vacuum
  9. Near-horizon geometry and attractor mechanism
  10. Existence of full black hole flows
  11. Comparison of index and entropy
  12. The $\bm{\mathcal{I}}$-extremization principle
  13. AdS$_{\bm 4} \times \bm{S^6/}$D2$_{\bm k}$ correspondence
  14. Supergravity details
  15. Dyonic STU model
  16. ...and 5 more sections

Figures (1)

  • Figure 1: Sequence of consistent truncations from massive type IIA supergravity in ten dimensions, to the dyonic STU model in four dimensions.