The 5d Superconformal Index at Large $N$ and Black Holes

Abstract

We study the large $N$ limit of the superconformal index of a large class of 5d $\mathcal{N}=1$ superconformal field theories and show it is given by the square of the partition function on the squashed five-sphere. We show this simple relation implies a Cardy formula in 5d, which is valid in an "extended" regime in which fugacities are finite and $N$ is large. For theories with weakly coupled gravity duals we conjecture this large $N$ Cardy formula universally accounts for the microscopic entropy of spinning black holes in AdS${}_6$. We check this explicitly for known black hole solutions in massive type IIA and type IIB string theory, carrying two angular momenta and one electric charge, and predict the entropy of black holes carrying multiple electric charges, yet to be constructed. We also discuss large $N$ properties of the $S_b^3\times {\Sigma }_{\mathfrak{g}}$ partition function, extending previous results to theories with type IIB duals.

28 pages; v2: 30 pages, References added and typos corrected (published version); v3: Typos corrected and references updated

References in corpus (12)

• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• 5-dim Superconformal Index with Enhanced En Global Symmetry
• M5-Branes, D4-Branes and Quantum 5D super-Yang-Mills
• Cardy Formulae for SUSY Theories in d=4 and d=6
• Supersymmetric Gauge Theories on the Five-Sphere
• Quantum Black Hole Entropy from 4d Supersymmetric Cardy formula
• Cardy-like asymptotics of the 4d $\mathcal{N}=4$ index and AdS${}_5$ blackholes
• Universal RG Flows Across Dimensions and Holography
• Supersymmetric gauge theories on squashed five-spheres and their gravity duals
• The gravity dual of supersymmetric gauge theories on a squashed five-sphere
• Supersymmetric AdS${}_7$ and AdS${}_6$ vacua and their consistent truncations with vector multiplets

Cited by in corpus (12)

• AdS black holes and finite N indices
• Sub-leading Structures in Superconformal Indices: Subdominant Saddles and Logarithmic Contributions
• D4-branes wrapped on a spindle
• Gravitational Cardy Limit and AdS Black Hole Entropy
• Exact QFT duals of AdS black holes
• Phases of five-dimensional supersymmetric gauge theories
• Universal Entropy and Hawking Radiation of Near-Extremal AdS${}_4$ Black Holes
• Black holes and Large $N$ complex saddles in 3D-3D correspondence
• Thermodynamics of BPS and Near-BPS AdS6 Black Holes
• Off-shell phase diagram of BPS black holes in AdS${}_5$
• 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