Supersymmetric $Ad{S}_6$ black holes from $F(4)$ gauged supergravity

Abstract

In $F(4)$ gauged supergravity in six dimensions, we study supersymmetric $Ad{S}_6$ black holes with various horizon geometries. We find a new $Ad{S}_2\times {\Sigma }_{{\mathfrak{g}}_1}\times {\Sigma }_{{\mathfrak{g}}_2}$ 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 $Ad{S}_6$ boundary and the $Ad{S}_2\times {\Sigma }_{{\mathfrak{g}}_1}\times {\Sigma }_{{\mathfrak{g}}_2}$ 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 ${\Sigma }_{{\mathfrak{g}}_1}\times {\Sigma }_{{\mathfrak{g}}_2}\times S^1$ 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.

v3: 17 pages, 2 figures. Title changed. Previous title was "D4-branes wrapped on supersymmetric four-cycles". Numerical black hole solutions added. Published version

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• Universal RG Flows Across Dimensions and Holography
• Topologically twisted indices in five dimensions and holography
• 5d Partition Functions with A Twist
• Supersymmetric AdS${}_7$ and AdS${}_6$ vacua and their minimal consistent truncations from exceptional field theory
• Gauged Six-Dimensional Supergravity from Warped IIB Reductions

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