Matrix models from black hole geometries

A bstract Supersymmetric, magnetically charged (and possibly accelerating) black holes in AdS 4 that uplift on Sasaki-Einstein manifolds Y 7 to M-theory have a dual matrix model description. The matrix model in turn arises by localization of the 3d N N = 2 SCFTs, dual to the AdS 4 vacuum, on the black hole horizon geometry, which is a Riemann surface Σ g (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 AdS 2 × Y 9 , the internal space Y 9 being a Y 7 fibration over Σ g (or Σ). Moreover, we argue that the points where ρ ′ ( t ) is discontinuous match with the classical action of BPS probe M2-branes wrapping AdS 2 and the M-theory circle. We illustrate our findings with the ABJM and ADHM theories, whose duals have Y 7 = S 7 / ℤ k , and some of their flavoured variants corresponding to other toric Y 7 .