A. Mironov, A. Oreshina, A. Popolitov, “$\beta$-WLZZ models from $\beta$-ensemble integrals directly”, Pis'ma v Zh. Èksper. Teoret. Fiz., 2024, Volume 120, Issue 1,Pages 62

This article is cited in 9 papers

METHODS OF THEORETICAL PHYSICS

$\beta$-WLZZ models from $\beta$-ensemble integrals directly

A. Mironov^abc, A. Oreshina^dbc, A. Popolitov^dbc

^a Lebedev Physical Institute, Russian Academy of Sciences, 119991, Moscow, Russia
^b National Research Center Kurchatov Institute, 123182, Moscow, Russia
^c Institute for Information Transmission Problems, Russian Academy of Sciences, 127994, Moscow, Russia
^d Moscow Institute of Physics and Technology (National Research University), 141701, Dolgoprudnyi, Moscow region, Russia

Abstract: Recently, we performed a two $\beta $-ensemble realization of the series of $\beta $-deformed WLZZ matrix models involving $\beta $-deformed Harish–Chandra–Itzykson–Zuber integrals. The realization was derived and studied by using Ward identities, which do not allow one to fix integration contours, these latter were chosen to be real axis for one $\beta $-ensemble and imaginary axis for the other one based on some particular checks. Here, we evaluate the $\beta $-ensemble integrals directly using a conjecture by I.G. Macdonald, and explain that another choice of integration contours is also possible.

Received: 18.05.2024
Revised: 29.05.2024
Accepted: 30.05.2024

DOI: 10.31857/S1234567824130111