Compact holography via polarized IKKT

Abstract

The polarized IKKT matrix model is a $U(N)$ supersymmetric matrix integral proposed to be dual to an $N$ D-instanton sector of Euclidean type IIB string theory. We show a direct path from matrix model saddles to supergravity saddles: matrix model resolvent $\to$ holomorphic function $\to$ 2D Coulomb potential $\to$ 4D Coulomb potential $\to$ supergravity fields, where the last step was previously described. Here, the 2D electrostatics picture is an exact finite $N$ reformulation of a localization deformation of the matrix model that gives a constrained gas of dipoles in a background field. We show a matching between supergravity and matrix model on-shell actions and protected observables for all saddles. We show that the supergravity saddles have a compact and non-singular metric in string frame with the Einstein frame asymptotic region replaced by a pointlike D-instanton source. We provide evidence that the physics of particular gravity saddles can be obtained through restricting the domain of the matrix model integral to a basin associated with the corresponding matrix model saddle. We describe certain large $N$ decoupling limits where families of the saddles decouple from the rest to give the gravity duals of certain higher-dimensional field theories.