Logarithmic potential beta-ensembles and Feynman graphs

Abstract

We present the diagrammatic technique for calculating the free energy of the matrix eigenvalue model (the model with arbitrary power beta by the Vandermonde) to all orders of 1/N expansion in the case where the limiting eigenvalue distribution spans arbitrary (but fixed) number of disjoint intervals (curves) and when logarithmic terms are present. This diagrammatic technique is corrected and refined as compared to our first paper with B.Eynard of year 2006.

17 pages, 20 figures in text; paper in honor of A.A.Slavnov's 70th birthday

References in corpus (5)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• On non-conformal limit of the AGT relations
• The Power of Nekrasov Functions
• Zamolodchikov asymptotic formula and instanton expansion in N=2 SUSY N_f=2N_c QCD

Cited by in corpus (9)

• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• A direct proof of AGT conjecture at beta = 1
• Explicit examples of DIM constraints for network matrix models
• The uses of the refined matrix model recursion
• Quantum curves and conformal field theory
• Irregular conformal block, spectral curve and flow equations
• Challenges of beta-deformation
• Genus one correction to Seiberg-Witten prepotential from β-deformed matrix model
• Irregular Conformal States and Spectral Curve: Irregular Matrix Model Approach