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arXiv · 1902.06619

Cardy-like asymptotics of the 4d $\mathcal{N}=4$ index and AdS$_5$ blackholes

Arash Arabi Ardehali
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Abstract

Choi, Kim, Kim, and Nahmgoong have recently pioneered analyzing a Cardy-like limit of the superconformal index of the 4d $\mathcal{N}=4$ theory with complexified fugacities which encodes the entropy of the dual supersymmetric AdS$_5$ blackholes. Here we study the Cardy-like asymptotics of the index within the rigorous framework of elliptic hypergeometric integrals, thereby filling a gap in their derivation of the blackhole entropy function, finding a new blackhole saddle-point, and demonstrating novel bifurcation phenomena in the asymptotics of the index as a function of fugacity phases. We also comment on the relevance of the supersymmetric Casimir energy to the blackhole entropy function in the present context.

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Arash Arabi Ardehali. 2019-02-18. Cardy-like asymptotics of the 4d $\mathcal{N}=4$ index and AdS$_5$ blackholes. https://doi.org/10.1007/jhep06(2019)134

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