Geometric transitions and integrable systems

TY - JOUR

T1 - Geometric transitions and integrable systems

AU - Diaconescu, D. E.

AU - Dijkgraaf, R.

AU - Donagi, R.

AU - Hofman, C.

AU - Pantev, T.

N1 - Funding Information: We are very grateful to Bogdan Florea and Antonella Grassi for collaboration at an early stage of the project and many useful discussions. We would also like to thank Jacques Distler, Sheldon Katz, Balázs Szendröi and Cumrun Vafa for helpful discussions. D.-E.D. would also like to acknowledge the partial support of the Alfred P. Sloan foundation and the hospitality of KITP Santa Barbara and The Aspen Center for Physics where part of this work was performed. The research of R.D. was supported by a NWO Spinoza grant and the FOM program String Theory and Quantum Gravity. R.D. was partially supported by NSF grant DMS 0104354 and FRG grant 0139799 for “The Geometry of Superstrings”. T.P. was partially supported by NSF grants FRG 0139799 and DMS 0403884. The work of C.M.H. was supported in part by a Marie Curie Fellowship under contract MEIF-CT-2003-500687, the Israel-US Binational Science Foundation, the ISF Centers of Excellence Program and Minerva.

PY - 2006/9/25

Y1 - 2006/9/25

N2 - We consider 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 A1 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 A1 Hitchin system therefore proving genus zero large N duality for this class of transitions.

AB - We consider 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 A1 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 A1 Hitchin system therefore proving genus zero large N duality for this class of transitions.

UR - https://www.scopus.com/pages/publications/33746903208

UR - https://www.scopus.com/pages/publications/33746903208#tab=citedBy

U2 - 10.1016/j.nuclphysb.2006.04.016

DO - 10.1016/j.nuclphysb.2006.04.016

M3 - Article

SN - 0550-3213

VL - 752

SP - 329

EP - 390

JO - Nuclear Physics B

JF - Nuclear Physics B

IS - 3

ER -