Geometric transitions and 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.

arXiv comment70 pages, 1 figure; version two: minor changes

References in corpus (21)

• Perturbative Gauge Theory As A String Theory In Twistor Space
• Matrix Models, Topological Strings, and Supersymmetric Gauge Theories
• The Topological Vertex
• Topological Strings and Integrable Hierarchies
• On Geometry and Matrix Models
• Mirror symmetry, Langlands duality, and the Hitchin system
• Open string instantons and superpotentials
• D-branes, Categories and N=1 Supersymmetry
• Enhanced Gauge Symmetry in Type II String Theory
• D-Branes, Derived Categories, and Grothendieck Groups
• Derived Categories and Zero-Brane Stability
• D-branes, open string vertex operators, and Ext groups
• Computation of Superpotentials for D-Branes
• Mirror symmetry for open strings
• Cubics, Integrable Systems, and Calabi-Yau Threefolds
• Holomorphic matrix models
• Enhanced D-Brane Categories from String Field Theory
• Generalized complexes and string field theory
• Unitarity, D-brane dynamics and D-brane categories
• Special geometry of local Calabi-Yau manifolds and superpotentials from holomorphic matrix models
• Geometric Transitions and Mixed Hodge Structures

Cited by in corpus (18)

• T-Branes and Geometry
• T-Branes at the Limits of Geometry
• T-Branes and $G_2$ Backgrounds
• Quiver algebras as Fukaya categories
• Sheaves on fibered threefolds and quiver sheaves
• Conifold geometries, topological strings and multi-matrix models
• Langlands duality for Hitchin systems
• Finiteness of Flux Vacua from Geometric Transitions
• Intermediate Jacobians and ADE Hitchin Systems
• Conifold geometries, matrix models and quantum solutions
• Donagi-Markman cubic for the generalised Hitchin system
• Calabi-Yau orbifolds over Hitchin bases
• Meromorphic Higgs bundles And Related Geometries
• Geometric Transitions and Mixed Hodge Structures
• Some comments on the local curve (B-side)
• Analytic equivalence of geometric transitions
• Aspects of Calabi-Yau Integrable and Hitchin Systems
• Frobenius manifolds and algebraic integrability