Large N Duality, Lens Spaces and the Chern-Simons Matrix Model

TL;DR

This paper demonstrates a precise match between the spectral curve of a Chern-Simons matrix model on lens spaces and the mirror Riemann surface of a related Calabi-Yau geometry, providing evidence for large N duality.

Contribution

It establishes the first check of the A-model large N duality for T^{*}(S^{3}/ ext{Z}_p) with p>2 by linking matrix model spectral curves to mirror symmetry geometry.

Findings

Spectral curve matches the mirror Riemann surface of the orbifolded conifold.

Provides evidence for large N duality in the context of lens spaces.

Connects Chern-Simons matrix models with mirror symmetry in string theory.

Abstract

We demonsrate that the spectral curve of the matrix model for Chern-Simons theory on the Lens space S^{3}/\ZZ_p is precisely the Riemann surface which appears in the mirror to the blownup, orbifolded conifold. This provides the first check of the $A$-model large $N$ duality for T^{*}(S^{3}/\ZZ_p), p>2.