Theory space of one unitary matrix model and its critical behavior associated with Argyres-Douglas theory

TL;DR

This paper explores the critical behavior of a class of unitary matrix models with cosine potentials, revealing their connection to Argyres-Douglas theories and deriving associated scaling dimensions.

Contribution

It generalizes the critical points analysis of unitary matrix models to all cosine potentials, linking them to a family of Argyres-Douglas theories and computing their scaling operators.

Findings

Identified critical points for all cosine potentials in the matrix model.

Derived scaling dimensions matching those of (A_1, A_{4k-1}) Argyres-Douglas theories.

Connected matrix model critical behavior with specific AD theories.

Abstract

The lowest critical point of one unitary matrix model with cosine plus logarithmic potential is known to correspond with the $(A_1, A_3)$ Argyres-Douglas (AD) theory and its double scaling limit derives the Painlev\'{e} II equation with parameter. Here, we consider the critical points associated with all cosine potentials and determine the scaling operators, their vevs and their scaling dimensions from perturbed string equations at planar level. These dimensions agree with those of $(A_1,A_{4k-1})$ AD theory.