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

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

1993-06-08

arxiv.org/abs/hep-th/9306043v1

Phys.Lett. B314 (1993) 197-205

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/0370-2693(93)90449-R

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.

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