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

Yu. Makeenko
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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.

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Yu. Makeenko. 1993-06-08. Some Remarks About the Two-Matrix Penner Model and the Kazakov-Migdal Model. https://doi.org/10.1016/0370-2693(93)90449-r

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