Singularities of N=1 Supersymmetric Gauge Theory and Matrix Models

TL;DR

This paper investigates singular vacua in N=1 supersymmetric U(N) gauge theories with adjoint matter, analyzing their structure and the limitations of matrix model descriptions at these points.

Contribution

It provides a detailed study of singularities in N=1 gauge theories using matrix models and strong-coupling methods, highlighting where the matrix model approach fails.

Findings

Matrix model descriptions break down at certain singular vacua.

Identified specific singularities in the n=1 branch and intersections with n=2 branches.

Explored N=1 Argyres-Douglas points and their properties.

Abstract

In N=1 supersymmetric U(N) gauge theory with adjoint matter $\Phi$ and polynomial tree-level superpotential $W(\Phi)$, the massless fluctuations about each quantum vacuum are generically described by $U(1)^n$ gauge theory for some n. However, by tuning the parameters of $W(\Phi)$ to non-generic values, we can reach singular vacua where additional fields become massless. Using both the matrix model prescription and the strong-coupling approach, we study in detail three examples of such singularities: the singularities of the n=1 branch, intersections of n=1 and n=2 branches, and a class of N=1 Argyres-Douglas points. In all three examples, we find that the matrix model description of the low-energy physics breaks down in some way at the singularity.