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${}_4$.

v1: 40 pages; v2: minor revisions; v3: references updated; v4: added footnote 3, 4 and 10, references updated

References in corpus (22)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• Supersymmetric multi-charge AdS_5 black holes
• Summing Up All Genus Free Energy of ABJM Matrix Model
• Superconformal Indices for $\mathcal{N}=6$ Chern Simons Theories
• Superconformal indices of three-dimensional theories related by mirror symmetry
• Quantum Black Hole Entropy from 4d Supersymmetric Cardy formula
• The Unreasonable Effectiveness of Higher-Derivative Supergravity in AdS${}_4$ Holography
• Cardy-like asymptotics of the 4d $\mathcal{N}=4$ index and AdS${}_5$ blackholes
• Universal RG Flows Across Dimensions and Holography
• EFT and the SUSY Index on the 2nd Sheet
• M-theoretic matrix models
• Sub-leading Structures in Superconformal Indices: Subdominant Saddles and Logarithmic Contributions
• Corrections to AdS${}_5$ Black Hole Thermodynamics from Higher-Derivative Supergravity
• Residues, modularity, and the Cardy limit of the 4d $\mathcal{N}=4$ superconformal index
• Delayed Deconfinement and the Hawking-Page Transition
• Higher-Derivative Corrections and AdS${}_5$ Black Holes
• Factorization of log-corrections in AdS${}_4$/CFT${}_3$ from supergravity localization
• ABJM at finite $N$ via 4d supergravity
• 4d N=2 supergravity observables from Nekrasov-like partition functions
• Decomposition of BPS Moduli Spaces and Asymptotics of Supersymmetric Partition Functions
• The Embedding of Gauged STU Supergravity in Eleven Dimensions

Cited by in corpus (8)

• Supersymmetric phases of AdS${}_4$/CFT${}_3$
• 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