Some Remarks About the Two-Matrix Penner Model and the Kazakov-Migdal Model

Abstract

I consider the Hermitean two-matrix model with a logarithmic potential which is associated in the one-matrix case with the Penner model. Using loop equations I find an explicit solution of the model at large N (or in the spherical approximation) and demonstrate that it solves the corresponding Riemann-Hilbert problem. I construct the potential of the Kazakov-Migdal model on a D-dimensional lattice, which turns out to be a sum of two logarithms as well, whose large-N solution is given by the same formulas. In the "naive" continuum limit this potential recovers in D<4 dimensions the standard scalar theory with quartic self-interaction. I exploit the solution to calculate explicitly the pair correlator of gauge fields in the Kazakov-Migdal model with the logarithmic potential.

Latex, 13 pages, NBI-HE-93-28

References in corpus (10)

• Rational Theories of 2D Gravity from the Two-Matrix Model
• Induced QCD at Large N
• Generalized Kontsevich Model Versus Toda Hierarchy and Discrete Matrix Models
• Combinatorial Solution of the Two-Matrix Model
• Exact Solution of Induced Lattice Gauge Theory at Large $N$
• A Hint on the External Field Problem for Matrix Models
• Some Remarks About Induced QCD
• The Large-$N$ Limit of the Two-Hermitian-matrix model by the hidden BRST method
• Mixed Model of Induced QCD
• Matrix Models of Induced Large-N QCD

Cited by in corpus (12)

• Fermionic Matrix Models
• Generalized Penner models to all genera
• Coloring Random Triangulations
• Kazakov--Migdal Model with Logarithmic Potential and the Double Penner Matrix Model
• Strings, Matrix Models, and Meanders
• Kosterlitz--Thouless Phase Transitions on Discretized Random Surfaces
• Two-logarithm matrix model with an external field
• Gross-Witten-Wadia Phase Transition in Induced QCD on the Graph
• A Remark on the Renormalization Group Equation for the Penner Model
• Large N Matrix Hyperspheres and the Gauge-Gravity Correspondence
• The Spatial Dynamics in Kazakov--Migdal Model
• Eigenvalue Dynamics and the Matrix Chain