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.

v4: 27 pages, 4 figures; comments added on the center symmetry breaking

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Cited by in corpus (37)

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• Sub-leading Structures in Superconformal Indices: Subdominant Saddles and Logarithmic Contributions
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• The large-$N$ limit of the 4d $\mathcal{N}=1$ superconformal index
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• Exact Stringy Microstates from Gauge Theories
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• Stringy corrections to the entropy of electrically charged supersymmetric black holes with ${\mathrm{AdS}}_5\times S^5$ asymptotics
• Supersymmetric phases of AdS${}_4$/CFT${}_3$
• Decomposition of BPS Moduli Spaces and Asymptotics of Supersymmetric Partition Functions
• 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
• Classification of large N superconformal gauge theories with a dense spectrum
• The 5d Superconformal Index at Large $N$ and Black Holes
• Quantum Phases of $4d$ $SU(N)$ $\mathcal{N}=4$ SYM
• Toward an Effective CFT${}_2$ from $\mathcal{N}=4$ Super Yang-Mills and Aspects of Hawking Radiation
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• Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs
• Supersymmetric zeta functions and determinants
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• Large $N$ limits of supersymmetric quantum field theories: A pedagogical overview
• Off-shell phase diagram of BPS black holes in AdS${}_5$
• Explorations of Universality in the Entropy and Hawking Radiation of Non-Extremal Kerr AdS${}_4$ Black Holes