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

References in corpus (8)

• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Supersymmetric multi-charge AdS_5 black holes
• Cardy Formulae for SUSY Theories in d=4 and d=6
• Localization on Hopf surfaces
• Comments on 1/16 BPS Quantum States and Classical Configurations
• $c-a$ from the $N=1$ superconformal index

Cited by in corpus (2)

• Black hole superpotential as a unifying entropy function and BPS thermodynamics
• Confinement and Graded Partition Functions for $\mathcal{N}=4$ SYM