Irregular conformal block and its matrix model

TL;DR

This paper introduces a new matrix model for irregular conformal blocks of odd degree, extending previous methods limited to even degree, and computes its partition function.

Contribution

It proposes a novel matrix model with a square root factor in the potential for odd degree irregular conformal blocks, expanding the computational toolkit.

Findings

Derived the partition function for the new matrix model.

Extended the applicability of matrix model methods to odd degree irregular singularities.

Provided explicit calculations demonstrating the model's validity.

Abstract

Irregular conformal block is a new tool to study Argyres-Douglas theory, whose irregular vector is represented as a simultaneous eigenstate of a set of positive Virasoro generators. One way to find the irregular conformal block is to use the partition function of the \beta-ensemble of hermitian matrix model. So far the method is limited to the case of irregular singularity of even degree. In this letter, we present a new matrix model for the case of odd degree and calculate its partition function. The model is different from the previous one in that its potential has additional factor of square root of matrix.