Matrix models for irregular conformal blocks and Argyres-Douglas theories

TL;DR

This paper constructs matrix models that reproduce irregular conformal blocks of Liouville theory, providing insights into Argyres-Douglas theories and extending the understanding of conformal blocks beyond regular cases.

Contribution

It introduces new matrix models with logarithmic and rational potentials that correspond to irregular conformal blocks, linking them to Argyres-Douglas theories.

Findings

Matrix models reproduce irregular conformal blocks on the sphere.

Potential includes both logarithmic and rational terms.

Connection established between matrix models and Argyres-Douglas theories.

Abstract

As regular conformal blocks describe the N=2 superconformal gauge theories in four dimensions, irregular conformal blocks are expected to reproduce the instanton partition functions of the Argyres-Douglas theories. In this paper, we construct matrix models which reproduce the irregular conformal conformal blocks of the Liouville theory on sphere, by taking a colliding limit of the Penner-type matrix models. The resulting matrix models have not only logarithmic terms but also rational terms in the potential. We also discuss their relation to the Argyres-Douglas type theories.