Conifold geometries, topological strings and multi-matrix models

Abstract

We study open B-model representing D-branes on 2-cycles of local Calabi--Yau geometries. To this end we work out a reduction technique linking D-branes partition functions and multi-matrix models in the case of conifold geometries so that the matrix potential is related to the complex moduli of the conifold. We study the geometric engineering of the multi-matrix models and focus on two-matrix models with bilinear couplings. We show how to solve this models in an exact way, without resorting to the customary saddle point/large N approximation. The method consists of solving the quantum equations of motion and using the flow equations of the underlying integrable hierarchy to derive explicit expressions for correlators. Finally we show how to incorporate in this formalism the description of several group of D-branes wrapped around different cycles.

35 pages, 5.3 and 6 revised

References in corpus (38)

• 2D Gravity and Random Matrices
• Superconformal Field Theory on Threebranes at a Calabi-Yau Singularity
• Matrix Models, Topological Strings, and Supersymmetric Gauge Theories
• Topological Strings and Integrable Hierarchies
• All genus correlation functions for the hermitian 1-matrix model
• On Geometry and Matrix Models
• Mirror Symmetry, D-Branes and Counting Holomorphic Discs
• A Large N Duality via a Geometric Transition
• Open string instantons and superpotentials
• Hermitean matrix model free energy: Feynman graph technique for all genera
• Gravity Duals of Fractional Branes and Logarithmic RG Flow
• Higher genus correlators for the hermitian matrix model with multiple cuts
• Lectures on 2D gravity and 2D string theory (TASI 1992)
• Les Houches lectures on matrix models and topological strings
• Rational Theories of 2D Gravity from the Two-Matrix Model
• Geometric Transitions and N=1 Quiver Theories
• Large N expansion of the 2-matrix model
• Solving Virasoro Constraints in Matrix Models
• Conformal Field Theory Techniques in Random Matrix models
• N=1 Supersymmetry, Deconstruction, and Bosonic Gauge Theories
• Gauge Invariant Matrix Model for the Â-D-Ê Closed Strings
• Combinatorial Solution of the Two-Matrix Model
• Unified description of correlators in non-Gaussian phases of Hermitean matrix model
• From Virasoro Constraints in Kontsevich's Model to $\mathcal{W}$-constraints in 2-matrix Models
• Genus one correlation to multi-cut matrix model solutions
• Free Energy of the Two-Matrix Model/dToda Tau-Function
• Geometric transitions and integrable systems
• Genus one contribution to free energy in hermitian two-matrix model
• Solvable Matrix Models
• Topological Symmetry of forms, N=1 Supersymmetry and S-duality on Special Manifolds
• Extended Toda lattice hierarchy, extended two-matrix model and c=1 string theory
• Loop equations for the semiclassical 2-matrix model with hard edges
• Integrable flows in c=1 string theory
• Special geometry of local Calabi-Yau manifolds and superpotentials from holomorphic matrix models
• Topological Field Theory Interpretations and LG Representation of c=1 String Theory
• Chern-Simons matrix model for local conifold
• Remarks on the Additional Symmetries and W-Constraints in the Generalized KdV Hierarchy
• Exact Correlators of Two-Matrix Models

Cited by in corpus (14)

• On the complete perturbative solution of one-matrix models
• Ward identities and combinatorics of rainbow tensor models
• Rainbow tensor model with enhanced symmetry and extreme melonic dominance
• Matrix Models and D-branes in Twistor String Theory
• On gauge/string correspondence and mirror symmetry
• Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory
• Conifold geometries, matrix models and quantum solutions
• Normal bundles to Laufer rational curves in local Calabi-Yau threefolds
• Counting conifolds and Dijkgraaf-Vafa matrix models for three matrices
• Flavour from partially resolved singularities
• Poisson structures on the conifold and local Calabi-Yau threefolds
• Brane superpotential and local Calabi-Yau manifolds
• Some comments on the local curve (B-side)
• Quantum chaos in 2D gravity