On-shell action and the Bekenstein-Hawking entropy of supersymmetric black holes in $AdS_6$
Recently, entropy of static supersymmetric black holes in $AdS_6$ was counted by topologically twisted index of five-dimensional superconformal field theories. However, the AdS/CFT dictionary states that the partition function of the boundary field theory is dual to the on-shell action of the bulk quantum gravity. In this paper, we aim to explain the micropcopic counting of black hole entropy by topologically twisted index. We calculate the renomalized on-shell action and show that the on-shell action equals minus the Bekenstein-Hawking entropy of the supersymmetric black holes in $AdS_6$.
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