Exact QFT duals of AdS black holes

Abstract

We construct large N saddle points of the matrix model for the $$ \mathcal{N} $$ N = 4 Yang- Mills index dual to the BPS black holes in AdS5 × S5, 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.

Higher-derivative corrections to flavoured BPS black hole thermodynamics and holography

“…This has been verified using different methods (including the Bethe ansatz method where the dominant configurations do not immediately arise as a saddle), see e.g. [3,[9][10][11][12][13][14][15][16][17][18]. A convenient way to isolate the contribution of the black hole saddle is to take a Cardy-like limit of small chemical potentials ω 1 , ω 2 → 0 after setting n 0 = ±1 and before taking the large-N limit.…”

“…The supersymmetric and extremal black hole [31] develops and infinitely long AdS 2 throat in its near-horizon geometry, for this reason in order to obtain a BPS 16 black hole thermodynamics it is convenient to turn on some temperature as a regulator. We will follow the method JHEP05(2024)276 of [1] and take the limit in two steps: first we impose the supersymmetry condition (but not the extremality one), evaluating the black hole on-shell action together with all related thermodynamic quantities in this regime, and only at the end we take the extremal limit.…”

Convexity restoration from hairy black hole in Einstein-Maxwell-charged scalar system in AdS

“…Schematically, one may say that while the Reissner-Nordstrom black hole is dual to Tr(Φ m ) with m ∼ O(N 2 ), the hairy black hole obtained as adding soliton should look like Tr(Φ m )(Tr(Φ 2 )) l . It may be interesting to study the implication of the phase transition in terms of the recent studies of black hole operators in CFTs[35,36].…”