Large $N$ Superconformal Indices for 3d Holographic SCFTs

Abstract

We study a limit of the superconformal index of the ABJM theory on $S^1\times S^2$ in which the size of the circle is much smaller than the radius of the two-sphere. We derive closed form expressions for the two leading terms in this Cardy-like limit which are valid to all orders in the $1/N$ expansion. These results are facilitated by a judicious rewriting of the superconformal index which establishes a connection with the Bethe Ansatz Equations that control the topologically twisted index. Using the same technique we extend these results to the superconformal index of another holographic theory: 3d $\mathcal{N}=4$ SYM coupled to one adjoint and $N_f$ fundamental hypermultiplets. We discuss the implications of our results for holography and the physics of charged rotating black holes in AdS${}_4$.

arXiv commentv1: 40 pages; v2: minor revisions; v3: references updated; v4: added footnote 3, 4 and 10, references updated

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• Comments on ABJM free energy on $S^3$ at large $N$ and perturbative expansions in M-theory and string theory
• Magnetic charge and black hole supersymmetric quantum statistical relation
• Maximally symmetric nuts in 4d $\mathcal{N}=2$ higher derivative supergravity
• Giant Gravitons and Volume Minimisation
• Universal Cardy-Like Behavior of 3D Partition Functions from Supersymmetric Localization
• Large $N$ limits of supersymmetric quantum field theories: A pedagogical overview
• Explorations of Universality in the Entropy and Hawking Radiation of Non-Extremal Kerr AdS${}_4$ Black Holes