Abstract
AbstractWe present tau functions of the multi-component KP hierarchy whose integral is equal to the correlation function of the Wilson loops of the two-dimensional Yang–Mills (YM) model on a surface Σ (orientable case). By adding the simplest BKP tau to the integration measure we get the YM model on the non-orientable surface. The higher times of the tau functions are related to random matrices and also source matrices; the latter play the role of free parameters, and the mentioned integrals are integrals over ensembles of random matrices. We study the cases where the integral of the tau function is a tau function again—the tau function of different hierarchies—two-component KP and one-component BKP.KeywordsWilson loopsRandom matricesTau functionsBKP hierarchySchur polynomialsHypergeometric functionsRandom partitions2D YMMathematics Subject Classification (2010)05A1514N1017B8035Q5135Q5335Q5537K2037K30
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