Matrix Models, Argyres-Douglas singularities and double scaling limits

TL;DR

This paper constructs a specific N=1 gauge theory with a matrix model spectral curve exhibiting Argyres-Douglas singularities, analyzes the large N expansion's singularities, and proposes double scaling limits leading to non-critical string theories.

Contribution

It introduces a novel N=1 gauge theory with a spectral curve that develops Argyres-Douglas singularities and explores the associated double scaling limits for non-critical string theory connections.

Findings

Large N expansion is singular at Argyres-Douglas points.

Double scaling limits can be defined at these singularities.

Spectral curve degenerates into multiple cuts in the limit.

Abstract

We construct an N=1 theory with gauge group U(nN) and degree n+1 tree level superpotential whose matrix model spectral curve develops an A_{n+1} Argyres-Douglas singularity. We evaluate the coupling constants of the low-energy U(1)^n theory and show that the large N expansion is singular at the Argyres-Douglas points. Nevertheless, it is possible to define appropriate double scaling limits which are conjectured to yield four dimensional non-critical string theories as proposed by Ferrari. In the Argyres-Douglas limit the n-cut spectral curve degenerates into a solution with n/2 cuts for even n and (n+1)/2 cuts for odd n.