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Supersymmetric $AdS_6$ black holes from $F(4)$ gauged supergravity

Minwoo Suh

TL;DR

We study supersymmetric AdS6 black holes in six-dimensional F(4) gauged supergravity by wrapping D4-branes on supersymmetric four-cycles. The analysis yields new AdS2 horizons, including a product of two Riemann surfaces, and full interpolating solutions connecting AdS6 to AdS2 horizons. The entropy of these black holes matches the large-N topologically twisted index of 5d USp(2N) gauge theory on the corresponding product of Riemann surfaces times S1, validating the holographic correspondence. The work also identifies AdS2 horizons arising from additional horizons on Kähler four-cycles in Calabi-Yau fourfolds and Cayley four-cycles in Spin(7) manifolds, extending the spectrum of known solutions.

Abstract

In $F(4)$ gauged supergravity in six dimensions, we study supersymmetric $AdS_6$ black holes with various horizon geometries. We find a new $AdS_2\,\times\,Σ_{\mathfrak{g}_1}\timesΣ_{\mathfrak{g}_2}$ horizon solution with $\mathfrak{g}_1>1$ and $\mathfrak{g}_2>1$, and present the black hole solution numerically. The full black hole is an interpolating geometry between the asymptotically $AdS_6$ boundary and the $AdS_2\,\times\,Σ_{\mathfrak{g}_1}\timesΣ_{\mathfrak{g}_2}$ horizon. We calculate the Bekenstein-Hawking entropy of the black hole and find a match with the recently calculated topologically twisted index of 5d $USp(2N)$ gauge theory on $Σ_{\mathfrak{g}_1}\timesΣ_{\mathfrak{g}_2}\times{S}^1$ in the large $N$ limit. We also find black hole horizons of Kähler four-cycles in Calabi-Yau fourfolds and on Cayley four-cycles in $Spin(7)$ manifolds.

Supersymmetric $AdS_6$ black holes from $F(4)$ gauged supergravity

TL;DR

We study supersymmetric AdS6 black holes in six-dimensional F(4) gauged supergravity by wrapping D4-branes on supersymmetric four-cycles. The analysis yields new AdS2 horizons, including a product of two Riemann surfaces, and full interpolating solutions connecting AdS6 to AdS2 horizons. The entropy of these black holes matches the large-N topologically twisted index of 5d USp(2N) gauge theory on the corresponding product of Riemann surfaces times S1, validating the holographic correspondence. The work also identifies AdS2 horizons arising from additional horizons on Kähler four-cycles in Calabi-Yau fourfolds and Cayley four-cycles in Spin(7) manifolds, extending the spectrum of known solutions.

Abstract

In gauged supergravity in six dimensions, we study supersymmetric black holes with various horizon geometries. We find a new horizon solution with and , and present the black hole solution numerically. The full black hole is an interpolating geometry between the asymptotically boundary and the horizon. We calculate the Bekenstein-Hawking entropy of the black hole and find a match with the recently calculated topologically twisted index of 5d gauge theory on in the large limit. We also find black hole horizons of Kähler four-cycles in Calabi-Yau fourfolds and on Cayley four-cycles in manifolds.

Paper Structure

This paper contains 11 sections, 46 equations, 2 figures.

Table of Contents

  1. Introduction
  2. $F(4)$ gauged supergravity in six dimensions
  3. Black holes with $AdS_2\,\times\,\Sigma_{\mathfrak{g}_1}\times\Sigma_{\mathfrak{g}_2}$ horizon
  4. The supersymmetry equations
  5. The $AdS_2$ solution and entropy of black holes
  6. Numerical black hole solutions
  7. Black holes with other horizons
  8. Kähler four-cycles in Calabi-Yau fourfolds
  9. Cayley four-cycles in $Spin(7)$ manifolds
  10. Conclusions
  11. The equations of motion

Figures (2)

  • Figure 1: Numerical black hole solution with $m\,=\,\sqrt{2}$ and $g\,=\,3m$. The black straight lines are the values at the $AdS_2$ horizon given in \ref{['ads2sol']}.
  • Figure 2: Numerical black hole solution with $m\,=\,\sqrt{2}$ and $g\,=\,3m$. The black straight lines are the values at the $AdS_2$ horizon given in \ref{['cayleyads2']}.