Phases in WLZZ Matrix Models

TL;DR

This paper explores the solution space of Ward identities in WLZZ matrix models, focusing on how different integration contours in the matrix integral characterize these solutions, especially in the two-matrix model with a cubic potential.

Contribution

It provides a detailed analysis of the solution space of Ward identities in WLZZ models, highlighting the role of contour choices in the matrix integral for the two-matrix cubic potential case.

Findings

Solution space characterized by contour choices

Connection between Ward identities and matrix integral contours

Insights into the structure of WLZZ models

Abstract

We discuss the space of solutions to the Ward identities associated with the WLZZ models. We mostly concentrate on the case of these models described by a two-matrix model with the cubic potential in one of the matrices. We study how this space of solutions can be described by the freedom in choosing integration contours in the matrix integral.