Superconformal indices at large $N$ and the entropy of AdS${}_5$ $\times$ SE${}_5$ black holes

Abstract

The large $N$ limit of the four-dimensional superconformal index was computed and successfully compared to the entropy of a class of AdS${}_5$ black holes only in the particular case of equal angular momenta. Using the Bethe Ansatz formulation, we compute the index at large $N$ with arbitrary chemical potentials for all charges and angular momenta, for general $\mathcal{N}=1$ four-dimensional conformal theories with a holographic dual. We conjecture and bring some evidence that a particular universal contribution to the sum over Bethe vacua dominates the index at large $N$. For $\mathcal{N}=4$ SYM, this contribution correctly leads to the entropy of BPS Kerr-Newman black holes in AdS${}_5\times S^5$ for arbitrary values of the conserved charges, thus completing the microscopic derivation of their microstates. We also consider theories dual to AdS${}_5\times {\mathrm{SE}}_5$, where SE${}_5$ is a Sasaki-Einstein manifold. We first check our results against the so-called universal black hole. We then explicitly construct the near-horizon geometry of BPS Kerr-Newman black holes in AdS${}_5\times T^{1,1}$, charged under the baryonic symmetry of the conifold theory and with equal angular momenta. We compute the entropy of these black holes using the attractor mechanism and find complete agreement with the field theory predictions.

36 pages + appendices; v2: typos corrected, references added

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• Words to describe a black hole
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• Delayed Deconfinement and the Hawking-Page Transition
• Entropy function from toric geometry
• Exact Stringy Microstates from Gauge Theories
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• Exact QFT duals of AdS black holes
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• Root of unity asymptotics for Schur indices of 4d Lagrangian theories
• Expanding on the Cardy-like limit of the superconformal index of 4d $\mathcal{N}=1$ ABCD SCFTs
• S-duality in the Cardy-like limit of the superconformal index
• Uplifting dyonic AdS${}_4$ black holes on seven-dimensional Sasaki-Einstein manifolds
• Confinement and Graded Partition Functions for $\mathcal{N}=4$ SYM
• $\mathcal{I}$-extremization with baryonic charges
• Kerr-Newman black holes from $\mathcal{N}=1^{\ast }$
• The topologically twisted index of $\mathcal{N}=4$ SU($N$) Super-Yang-Mills theory and a black hole Farey tail
• Giant Gravitons and Volume Minimisation
• Hawking-Page transition on a spin chain
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