A matrix model for the topological string II: The spectral curve and mirror geometry

TL;DR

This paper explores the spectral curve of a matrix model for topological strings on toric Calabi-Yau manifolds, deriving the large volume limit of the BKMP conjecture linking Gromov-Witten invariants to mirror curve spectral invariants.

Contribution

It establishes a connection between the spectral curve of a matrix model and the mirror geometry, supporting the BKMP conjecture in the large volume limit.

Findings

Derived the spectral curve from the matrix model.

Connected Gromov-Witten invariants to spectral invariants.

Supported the BKMP conjecture in the large volume limit.

Abstract

In a previous paper, we presented a matrix model reproducing the topological string partition function on an arbitrary given toric Calabi-Yau manifold. Here, we study the spectral curve of our matrix model and thus derive, upon imposing certain minimality assumptions on the spectral curve, the large volume limit of the BKMP "remodeling the B-model" conjecture, the claim that Gromov-Witten invariants of any toric Calabi-Yau 3-fold coincide with the spectral invariants of its mirror curve.