Topological expansion and boundary conditions

Abstract

In this article, we compute the topological expansion of all possible mixed-traces in a hermitian two matrix model. In other words we give a recipe to compute the number of discrete surfaces of given genus, carrying an Ising model, and with all possible given boundary conditions. The method is recursive, and amounts to recursively cutting surfaces along interfaces. The result is best represented in a diagrammatic way, and is thus rather simple to use.

latex, 25 pages. few misprints corrected

References in corpus (13)

• 2D Gravity and Random Matrices
• All genus correlation functions for the hermitian 1-matrix model
• Matrix Model Calculations beyond the Spherical Limit
• Free energy topological expansion for the 2-matrix model
• Rational Theories of 2D Gravity from the Two-Matrix Model
• H(3)+ correlators from Liouville theory
• Large N expansion of the 2-matrix model
• H^+_3 WZNW model from Liouville field theory
• Combinatorial Solution of the Two-Matrix Model
• Eigenvalue distribution of large random matrices, from one matrix to several coupled matrices
• Master loop equations, free energy and correlations for the chain of matrices
• Topological expansion of the 2-matrix model correlation functions: diagrammatic rules for a residue formula
• Scattering of Long Folded Strings and Mixed Correlators in the Two-Matrix Model

Cited by in corpus (7)

• The matrix model version of AGT conjecture and CIV-DV prepotential
• A new continuum limit of matrix models
• CFT and topological recursion
• Blobbed topological recursion of the quartic Kontsevich model I: Loop equations and conjectures
• Enumeration of maps with self avoiding loops and the O(n) model on random lattices of all topologies
• Complete solution of the LSZ Model via Topological Recursion
• Non-homogenous disks in the chain of matrices