Matrix models from black hole geometries

Abstract

Abstract Supersymmetric, magnetically charged (and possibly accelerating) black holes in AdS4 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 $$ \mathcal{N} $$ = 2 SCFTs, dual to the AdS4 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 AdS2 × 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 AdS2 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.

Keywords

• AdS-CFT Correspondence
• Black Holes in String Theory
• Matrix Models
• Supersymmetric Gauge Theory