Ward identities and W-constraints in Generalized Kontsevich Model

TL;DR

This paper explores the relationship between Ward identities and W-constraints in the Generalized Kontsevich Model with specific potentials, establishing that Ward identities encompass W-constraints for the potential $X^4/4$ and suggesting similar connections for other potentials.

Contribution

It demonstrates that Ward identities include W-constraints in the $X^4/4$ potential case and proposes this relationship extends to models with potentials of the form $X^{(K+1)}/(K+1)$ for any $K \, \geq 2$.

Findings

Ward identities include W-constraints for the $X^4/4$ potential

The connection likely extends to potentials $X^{(K+1)}/(K+1)$ for $K\geq 2$

No other constraints are included in Ward identities for this model

Abstract

The connection is obtained between Ward identities and W-constraints in Generalized Kontsevich Model with the potential $X^4/4$. We show that Ward identities include W-constraints (and do not include any other constraints) for this potential and make some observations in favour of the same connection for the model with the potential of the form $X^{(K+1)}/(K+1)$ for any $K\geq 2$.