On-shell action and the Bekenstein-Hawking entropy of supersymmetric black holes in $AdS_6$

Understand

Recently, entropy of static supersymmetric black holes in $AdS_6$ was microscopically counted by the topologically twisted index of five-dimensional superconformal field theories.

• However, the AdS/CFT dictionary states that the partition function of the boundary field theory corresponds to the on-shell action of the bulk quantum gravity.
• In this paper, we aim to explain the microscopic counting of black hole entropy by the topologically twisted index.
• We calculate the renormalized on-shell action and show that the on-shell action equals the Bekenstein-Hawking entropy of the supersymmetric black holes in $AdS_6$.