Bubbling Calabi-Yau geometry from matrix models

TL;DR

This paper explores the connection between Wilson loops in Chern-Simons theory and bubbling geometries in topological string theory, deriving spectral curves that encode dual Calabi-Yau geometries, including new duals for lens spaces.

Contribution

It formulates multi-matrix models for Wilson loops in Chern-Simons theory on various manifolds and derives their spectral curves, revealing new dual geometries in topological string theory.

Findings

Spectral curves encode dual Calabi-Yau geometries.

New dual geometries for lens spaces are identified.

Matrix models successfully describe Wilson loop insertions.

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 insertion of an arbitrary representation. For each of these three manifolds we formulate a multi-matrix model whose partition function is the vev of the Wilson loop and compute the spectral curve. This spectral curve is the reduction to two dimensions of the mirror to a Calabi-Yau threefold which is the gravitational dual of the Wilson loop insertion. For lens spaces the dual geometries are new. We comment on a similar matrix model which appears in the context of Wilson loops in AdS/CFT.