Geometric transitions and integrable systems

Duiliu-Emanuel Diaconescu; Ron Donagi; Robbert Dijkgraaf; Christiaan Hofman; Tony Pantev

doi:10.1016/j.nuclphysb.2006.04.016

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arXiv · hep-th/0506196

Geometric transitions and integrable systems

Duiliu-Emanuel Diaconescu·Ron Donagi·Robbert Dijkgraaf·Christiaan Hofman·Tony Pantev

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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 $Σ$. 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 $Σ$. 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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Duiliu-Emanuel Diaconescu, Ron Donagi, Robbert Dijkgraaf, Christiaan Hofman, Tony Pantev. 2005-06-28. Geometric transitions and integrable systems. https://doi.org/10.1016/j.nuclphysb.2006.04.016

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