Branches of N=1 Vacua and Argyres-Douglas Points

TL;DR

This paper explores N=1 gauge theories near Argyres-Douglas points, identifying specific superpotentials that reproduce these critical points and suggesting a new class of N=1 superconformal field theories.

Contribution

It identifies superpotentials that generate N=2 AD points in N=1 theories and proposes a new class of N=1 superconformal field theories at these points.

Findings

Superpotentials W'(x)=x^N ± 2Λ^N reproduce AD points.

Certain vacua exhibit vanishing mass gap at AD points.

A possible N=1 superconformal field theory class is proposed.

Abstract

We study the N=1 version of Argyres-Douglas (AD) points by making use of the recent developments in understanding the dynamics of the chiral sector of N=1 gauge theories. We shall consider N=1 U(N) gauge theories with an adjoint matter and look for the tree-level superpotential W(x) which reproduces the N=2 AD points via the factorization equation relating the N=1 and N=2 curves. We find that the following superpotentials generate the N=2 AD points: (1) W'(x)=x^N \pm 2\Lambda^N, (2) W'(x)=x^n, N-1\ge n \ge N/2+1. In case (1) the physics is essentially the same as the N=2 theory even in the presence of the superpotential. There seems to be an underlying structure of N-reduced KP hierarchy in the system. Case (2) occurs at the intersection of a number of N=1 vacua with massless monopoles. This branch of vacua is characterized by having s_+=0 or s_-=0 where s_{\pm} denotes the number of double roots in P_N(x)\pm 2\Lambda^N. It is possible to show that the mass gap in fact vanishes at this AD point. We conjecture that it represents a new class of N=1 superconformal field theory.