Phases and triple(multiple) point: critical phenomena around the AD singularity

TL;DR

This paper investigates the critical phenomena and phase structure around the Argyres-Douglas singularity in ${ m extbf{N}}=2$ supersymmetric theories, revealing a phase diagram with three phases and a triple point through matrix model analysis.

Contribution

It introduces a detailed phase diagram with three phases and a triple point for ${ m extbf{N}}=2$ theories near the Argyres-Douglas singularity using matrix models and 0d-4d connection.

Findings

Identified three distinct phases with different eigenvalue distributions.

Mapped the phase diagram including a triple point.

Showed the transition line between 1- and 2-gap phases is multicritical.

Abstract

Continuing with our previous series of work, we present a case study of the critical phenomena around Argyres-Douglas singularity of ${\cal N} =2$ susy made at $(A_1, A_{4k-1} ), k =1, 2$ realized by one-unitary matrix model. We determine the phase diagram, which is recast into LEEA of $\mathcal{N}=2$, 4d gauge theory by the 0d-4d connection. There are three distinct phases, each corresponding to an eigenvalue distribution with 0, 1, and 2 gaps. These form an entire phase diagram with a triple point. Examining the behavior of the planar free energy, we show, among other things,that the transition line between 1- and 2-gap phases ending at the triple point is the $k=2$ multicritical one.