This article is cited in 12 papers

METHODS OF THEORETICAL PHYSICS

Virasoro versus superintegrability. Gaussian Hermitian model

A. Mironov^abc, V. Mishnyakov^abd, A. Morozov^dbc, R. Rashkov<sup>ef

a</sup> Lebedev Physics Institute, Russian Academy of Sciences, Moscow, 119991 Russia
^b Alikhanov Institute for Theoretical and Experimental Physics, National Research Center Kurchatov Institute, Moscow, 117218 Russia
^c Institute for Information Transmission Problems, Moscow, 127994 Russia
^d Moscow Institute of Physics and Technology (National Research University), Dolgoprudnyi, Moscow region, 141701 Russia
^e Institute for Theoretical Physics, Vienna University of Technology, Vienna, 1040 Austria
^f Department of Physics, Sofia University, Sofia, 1164 Bulgaria

Abstract: Relation between the Virasoro constraints and KP integrability (determinant formulas) for matrix models is a lasting mystery. We elaborate on the claim that the situation is improved when integrability is enhanced to superintegrability, i.e., to explicit formulas for Gaussian averages of characters. In this case, the Virasoro constraints are equivalent to simple recursive formulas, which have appropriate combinations of characters as their solutions. Moreover, one can easily separate dependence on the size of matrix, and deduce superintegrability from the Virasoro constraints. We describe one of the ways to do so for the Gaussian Hermitian matrix model. The result is a spectacularly elegant reformulation of Virasoro constraints as identities for the Schur functions evaluated at appropriate loci in the space of time-variables.

Received: 27.04.2021
Revised: 28.04.2021
Accepted: 28.04.2021

DOI: 10.31857/S1234567821110082

 English version: Journal of Experimental and Theoretical Physics Letters, 2021, 113:11, 728–732

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