The Spectral Curve of the Lens Space Matrix Model

TL;DR

This paper analyzes the spectral curve of the lens space matrix model related to topological string theory, revealing its structure as a p-cut single matrix model and exploring its implications for large N transitions and mirror symmetry.

Contribution

It provides an explicit solution for the resolvent and spectral curve of the matrix model describing the topological A-model on T^{*}(S^{3}/bZ_p), extending previous work.

Findings

The resolvent exhibits square root branch cuts.

The model is characterized as a p-cut single matrix model.

Connections to large N transitions and mirror symmetry are discussed.

Abstract

Following hep-th/0211098 we study the matrix model which describes the topological A-model on T^{*}(S^{3}/\ZZ_p). We show that the resolvent has square root branch cuts and it follows that this is a p cut single matrix model. We solve for the resolvent and find the spectral curve. We comment on how this is related to large N transitions and mirror symmetry.