Geometric transitions and integrable systems

TL;DR

This paper establishes a genus zero large N duality for a class of noncompact Calabi-Yau spaces, linking Hitchin integrable systems with generalized matrix models through geometric transitions.

Contribution

It demonstrates that the large N limit of a generalized matrix model corresponds to an $A_1$ Hitchin system, proving a new duality in string theory.

Findings

Large N limit governed by $A_1$ Hitchin system

Genus zero duality proven for new Calabi-Yau transitions

Open and closed string descriptions are connected via integrable systems

Abstract

We consider {\bf B}-model large $N$ duality for a new class of noncompact Calabi-Yau spaces modeled on the neighborhood of a ruled surface in a Calabi-Yau threefold. The closed string side of the transition is governed at genus zero by an $A_1$ Hitchin integrable system on a genus $g$ Riemann surface $\Sigma$. The open string side is described by a holomorphic Chern-Simons theory which reduces to a generalized matrix model in which the eigenvalues lie on the compact Riemann surface $\Sigma$. We show that the large $N$ planar limit of the generalized matrix model is governed by the same $A_1$ Hitchin system therefore proving genus zero large $N$ duality for this class of transitions.