Black holes in 4d $\mathcal{N}=4$ Super-Yang-Mills

Abstract

We resolve a long-standing question: does the four-dimensional $\mathcal{N}=4$ SU(N) Super-Yang-Mills theory on $S^3$ at large N contain enough states to account for the entropy of rotating electrically-charged BPS black holes in AdS${}_5$? Our answer is positive. We reconsider the large N limit of the superconformal index, using the Bethe Ansatz formulation, and find an exponentially large contribution which exactly reproduces the Bekenstein-Hawking entropy of the black holes of Gutowski-Reall. Besides, the large N limit exhibits a complicated structure, with many competing exponential contributions and Stokes lines, hinting at new physics.

arXiv comment33 pages + appendices, 4 figures; v2: references and clarifications added; v3: minor changes, conclusions unaltered

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• Logarithmic Corrections to the Entropy of Rotating Black Holes and Black Strings in AdS${}_5$
• The Surprising Effectiveness of Weyl Gravity in Probing Quantum Corrections to AdS Black Holes
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• Finite $N$ indices and the giant graviton expansion
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• Root of unity asymptotics for Schur indices of 4d Lagrangian theories
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• S-duality in the Cardy-like limit of the superconformal index
• Expanding on the Cardy-like limit of the superconformal index of 4d $\mathcal{N}=1$ ABCD SCFTs
• Confinement and Graded Partition Functions for $\mathcal{N}=4$ SYM
• The large-N partition function for non-parity-invariant Chern-Simons-matter theories
• Thermodynamics of BPS and Near-BPS AdS6 Black Holes
• All separable supersymmetric AdS${}_5$ black holes
• Witten index of BMN matrix quantum mechanics
• Wrapped M5-branes and AdS${}_5$ Black Holes
• The topologically twisted index of $\mathcal{N}=4$ SU($N$) Super-Yang-Mills theory and a black hole Farey tail
• Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory
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