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
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关于二矩阵Penner模型和Kazakov-Migdal模型的一些评论
DOI：
10.1016/0370-2693(93)90449-r
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
Y. Makeenko
中科院分区：
文献类型：
--
作者：
Y. Makeenko
我考虑具有对数势的厄米特双矩阵模型，它在单矩阵的情况下与Penner模型相关。利用回路方程，我求出了该模型在大N下(或在球面近似下)的显式解，并证明了它解决了相应的Riemann-Hilbert问题。我在D维格子上构造了Kazakov-Migdal模型的势，证明它也是两个对数的和，它的大N解由相同的公式给出。在“幼稚的”连续体极限中，这个势能在D>；4维中恢复标准标量理论与四次自作用。利用该解显式计算了具有对数势的Kazakov-Migdal模型中规范场的对关联子。
I consider the hermitian 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.