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

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.

arXiv commentv4: 27 pages, 4 figures; comments added on the center symmetry breaking

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• The asymptotic growth of states of the 4d N=1 superconformal index
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• Stringy corrections to the entropy of electrically charged supersymmetric black holes with ${\mathrm{AdS}}_5\times S^5$ asymptotics
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• Supersymmetric phases of AdS${}_4$/CFT${}_3$
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• Logarithmic Corrections to the Entropy of Rotating Black Holes and Black Strings in AdS${}_5$
• Higher-derivative corrections to flavoured BPS black hole thermodynamics and holography
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• S-duality in the Cardy-like limit of the superconformal index
• Confinement and Graded Partition Functions for $\mathcal{N}=4$ SYM
• Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs
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• Hawking-Page transition on a spin chain
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