Geometric transitions and integrable systems

Details Geometric transitions and integrable systems Geometric transitions and integrable systems

2005-06-23

arxiv.org/abs/hep-th/0506196v2

Nucl.Phys. B752 (2006) 329-390

Physics

High Energy Physics

High Energy Physics - Theory

70 pages, 1 figure; version two: minor changes

Scientific paper

10.1016/j.nuclphysb.2006.04.016

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.

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