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- W2913384368 abstract "We study the canonical $mathrm{AdS}/mathrm{CFT}$ correspondence between 4d $SU(N)$ $mathcal{N}=4$ super Yang-Mills theory (SYM) and type IIB superstring theory on ${mathrm{AdS}}_{5}ifmmodetimeselsetexttimesfi{}{S}^{5}$. We analyze the supersymmetric index of the $mathcal{N}=4$ SYM on ${S}^{1}ifmmodetimeselsetexttimesfi{}{M}_{3}$ which counts supersymmetric states with fixed quantum numbers. We compute an asymptotic behavior of the index in the limit of shrinking ${S}^{1}$ for any $N$ by a refinement of the 4d supersymmetric Cardy formula. The asymptotic behavior for the superconformal index case (${M}_{3}={S}^{3}$) at large $N$ agrees with the Bekenstein-Hawking entropy of a rotating electrically charged Bogomolnyi-Prasad-Sommerfeld (BPS) black hole in ${mathrm{AdS}}_{5}$ via a Legendre transformation as recently shown in the literature. We also find that the agreement formally persists for finite $N$ if we slightly modify the $mathrm{AdS}/mathrm{CFT}$ dictionary between the Newton constant and $N$. This implies the existence of a nonrenormalization property of the black hole entropy against quantum corrections. We also study the cases with other gauge groups and additional matter and the orbifold $mathcal{N}=4$ SYM. It turns out that the entropies of all the CFT examples in this paper are universally given by $2ensuremath{pi}sqrt{{Q}_{1}{Q}_{2}+{Q}_{1}{Q}_{3}+{Q}_{2}{Q}_{3}ensuremath{-}2c({J}_{1}+{J}_{2})}$ with charges ${Q}_{1,2,3}$, angular momenta ${J}_{1,2}$, and central charge $c$. The results for other ${M}_{3}$ make predictions to the gravity side." @default.
- W2913384368 created "2019-02-21" @default.
- W2913384368 creator A5087588286 @default.
- W2913384368 date "2019-07-17" @default.
- W2913384368 modified "2023-10-14" @default.
- W2913384368 title "Quantum black hole entropy from 4d supersymmetric Cardy formula" @default.
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- W2913384368 doi "https://doi.org/10.1103/physrevd.100.026008" @default.
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