Exact QFT duals of AdS black holes

Abstract

We construct large $N$ saddle points of the matrix model for the $\mathcal{N}=4$ Yang-Mills index dual to the BPS black holes in $Ad{S}_5\times S^5$, in two different setups. When the two complex chemical potentials for the angular momenta are collinear, we find linear eigenvalue distributions which solve the large $N$ saddle point equation. When the chemical potentials are not collinear, we find novel solutions given by areal eigenvalue distributions after slightly reformulating the saddle point problem. We also construct a class of multi-cut saddle points, showing that they sometimes admit nontrivial filling fractions. As a byproduct, we find that the Bethe ansatz equation emerges from our saddle point equation.

40 pages, 6 figures; v2

References in corpus (7)

• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Supersymmetric multi-charge AdS_5 black holes
• Supersymmetric states of N=4 Yang-Mills from giant gravitons
• Comments on 1/16 BPS Quantum States and Classical Configurations
• The Hilbert Series of Adjoint SQCD
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Cited by in corpus (7)

• BPS Chaos
• Higher-derivative corrections to flavoured BPS black hole thermodynamics and holography
• Supersymmetric Grey Galaxies, Dual Dressed Black Holes and the Superconformal Index
• S-duality in the Cardy-like limit of the superconformal index
• Giant Gravitons and Volume Minimisation
• Large $N$ limits of supersymmetric quantum field theories: A pedagogical overview
• Off-shell phase diagram of BPS black holes in AdS${}_5$