Many-body integrable systems implied by WLZZ models

We provide some details about the recently discovered integrable systems implied by commutativity of Woperators along the rays on the plane of roots of w infinity-algebra. The simplest system of this type is the rational Calogero model, other systems escaped attention in the past. Existence of these systems is intimately tied to the very interesting WLZZ matrix models, which are now under intensive study. (c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.

Automated summary

This paper provides some details about recently discovered integrable systems implied by commutativity of W-operators along the rays on the plane of roots of the w infinity-algebra. The simplest system of this type is the rational Calogero model, while other systems have not received attention in the past. The existence of these systems is closely tied to the currently intensively studied WLZZ matrix models.