Exact Results for the Supersymmetric $G_2$ Gauge Theories

TL;DR

This work derives exact dynamical results for N=1 supersymmetric G2 gauge theories with N_f fundamental flavors, showing dynamically generated superpotentials for N_f≤3, a smooth quantum moduli space for N_f=4, and confinement without chiral symmetry breaking for N_f=5. For N_f≥6, the theory flows to a non-trivial interacting superconformal phase, with a discussion of a candidate dual description and the associated challenges of matching global symmetries. The analysis combines holomorphy, symmetry constraints, and explicit G2 group theory (including an SU(3) embedding) to map the classical moduli space to its quantum deformations. The results extend the understanding of exact dynamics in exceptional-gauge theories and highlight how quantum effects reorganize vacuum structure and phase behavior across N_f.

Abstract

We study the $N=1$ supersymmetric $G_2$ gauge theories with $N_f$ flavors of quarks in the fundamental vector representation. We find dynamically generated superpotentials, smooth quantum moduli space, quantum moduli space with additional mesons, non trivial IR fixed points.