Integrals of tau functions: A round dance tau function and multimatrix integrals

A. Yu. Orlov^{a, b}^,*

^aShirshov Institute of Oceanology, Russian Academy of Sciences, Moscow, Russia

^bAlikhanov Institute for Theoretical and Experimental Physics, National Research Center “Kurchatov Institute”, Moscow, Russia

email: *orlovs55@mail.ru

Received 20 November, 2022

Abstract— A multimatrix model can be built on two ingredients: the choice of an embedded graph and the choice of the integrand, that is, a tau function. We compare the simplest nontrivial tau function of the Toda lattice and the simplest nontrivial tau function of the \(\mathcal N\)-component Toda lattice in the context of their application to multimatrix integrals.

Keywords: tau function, special solution of the multicomponent KP hierarchy, embedded graph, Hurwitz number

DOI: 10.1134/S004057792306003X