The polarised IKKT matrix model

Abstract

We establish a correspondence between a supersymmetric mass deformation of the IKKT matrix integral at large N and a background of Euclidean type IIB string theory. Both sides have sixteen supersymmetries and an SO(3) × SO(7) symmetry. In the limit of large mass the integral is dominated by a fuzzy sphere saddle point. This saddle corresponds to a Euclidean D1-brane in a finite, Euclidean, ellipsoidal cavity. The cavity is supported by three-form NSNS flux that polarises N D-instantons into the D1-brane. We furthermore use supersymmetric localisation to show that the deformed matrix integral can be reduced to a moduli space integral, allowing exact results away from the large mass limit. At small mass the D1-branes can backreact on the geometry, and we discuss the possible formulation of a ‘timeless’ holography in such regimes.