Cardylike asymptotics of the 4d $\mathcal{N}=4$ index and AdS$_5$ blackholes
Abstract
Choi, Kim, Kim, and Nahmgoong have recently pioneered analyzing a Cardylike 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 Cardylike 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 saddlepoint, 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2019
 arXiv:
 arXiv:1902.06619
 Bibcode:
 2019arXiv190206619A
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 v4: 27 pages, 4 figures