Matrix models from black hole geometries

Abstract

Supersymmetric, magnetically charged (and possibly accelerating) black holes in AdS4 that uplift on Sasaki-Einstein manifolds Y7 to M-theory have a dual matrix model description. The matrix model in turn arises by localization of the 3d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 SCFTs, dual to the AdS4 vacuum, on the black hole horizon geometry, which is a Riemann surface Σg (or a spindle Σ). We identify the imaginary part t of the continuously distributed eigenvalues in the matrix model, and their density function ρ(t), with natural geometric quantities associated with the M-theory circle action U(1)M on the near-horizon geometry AdS2 × Y9, the internal space Y9 being a Y7 fibration over Σg (or Σ). Moreover, we argue that the points where ρ′(t) is discontinuous match with the classical action of BPS probe M2-branes wrapping AdS2 and the M-theory circle. We illustrate our findings with the ABJM and ADHM theories, whose duals have Y7 = S7/ℤk, and some of their flavoured variants corresponding to other toric Y7.