6 + 1 Vacua in Supersymmetric QCD with G_2 Gauge Group

TL;DR

This paper analyzes the vacuum structure of N=1 supersymmetric QCD with G_2 gauge group and chiral matter, revealing the number and nature of vacua depending on superpotential terms and couplings.

Contribution

It provides a detailed study of vacua in G_2 supersymmetric QCD, including the effects of Yukawa couplings and matter representations, extending understanding of vacuum configurations.

Findings

Six chirally asymmetric vacua with Yukawa term

Four vacua when Yukawa coupling vanishes

Presence of vacua at infinity and at finite moduli in extended models

Abstract

We consider N=1 supersymmetric QCD based on the G_2 gauge group and including 3 chiral matter 7-plets. In that case, the gauge symmetry is broken completely and the instanton-generated superpotential on the classical moduli space is present. If the theory involves the Yukawa term, there are six chirally asymmetric vacua. In the limit when the Yukawa coupling vanishes, two of the vacua run away to infinity and only 4 asymmetric vacuum states are left. Besides, a chirally symmetric state is always present. We consider also an O(7) model with 4 chiral multiplets in spinor representation. In that case, there are 4 extra "virtual vacua" dwelling at infinity of the moduli space. In a non-renormalizable theory involving a quartic term in the superpotential, they show up at finite moduli values.