Bubbling Calabi-Yau geometry from matrix models

Abstract

We study bubbling geometry in topological string theory. Specifically, we analyse Chern-Simons theory on both the 3-sphere and lens spaces in the presence of a Wilson loop of an arbitrary representation. For each three manifold, we formulate a multi-matrix model whose partition function is the Wilson loop vev and compute the spectral curve. This spectral curve is closely related to the Calabi-Yau threefold which is the gravitational dual of the Wilson loop. Namely, it is the reduction to two dimensions of the mirror to the Calabi-Yau. For lens spaces the dual geometries are new. We comment on a similar matrix model relevant for Wilson loops in AdS/CFT.