Irregular matrix model with $\mathcal W$ symmetry

TL;DR

This paper introduces an irregular matrix model with $ ext{W}_3$ and Virasoro symmetries, derived from Toda field theories, and computes its partition function using symmetry flow equations.

Contribution

It presents a new irregular matrix model with $ ext{W}_3$ and Virasoro symmetry, connecting Toda field theories and irregular modules.

Findings

Partition function evaluated via flow equations

Model captures irregular modules of $ ext{W}_3$ symmetry

Links Toda theories with matrix models

Abstract

We present the irregular matrix model which has contains $\mathcal{W}_3$ and Virasoro symmetry. The irregular matrix model is obtained using the colliding limit of the Toda field theories and produces the inner product between irregular modules of $\mathcal{W}_3$ symmetry. We evaluate the partition function using the flow equation which is the realization of the Virasoro and $\mathcal{W}$-symmetry.