From Virasoro Constraints in Kontsevich's Model to $\cal W$-constraints in 2-matrix Models

TL;DR

This paper demonstrates how Ward identities in Kontsevich-like matrix models establish a connection between potential degrees in asymmetric 2-matrix models and their associated $ ext{ extcal W}$-constraints, advancing understanding of matrix model symmetries.

Contribution

It provides a proof linking potential degrees to $ ext{ extcal W}$-constraints in asymmetric 2-matrix models using Ward identities.

Findings

Ward identities relate potential degree to $ ext{ extcal W}$-constraints

Proof confirms Gava and Narain's suggestion at the discrete matrix model level

Enhances understanding of symmetries in matrix models

Abstract

The Ward identities in Kontsevich-like 1-matrix models are used to prove at the level of discrete matrix models the suggestion of Gava and Narain, which relates the degree of potential in asymmetric 2-matrix model to the form of $\cal W$-constraints imposed on its partition function.