Some exact results in supersymmetric theories based on exceptional groups

TL;DR

This paper explores supersymmetric theories based on exceptional groups, specifically G2, analyzing their superpotentials, moduli spaces, and phases, revealing parallels with classical gauge theories and identifying exact results for various flavor numbers.

Contribution

It provides the first explicit analysis of supersymmetric G2 theories, including superpotentials, moduli spaces, and phase structures, expanding understanding of exceptional gauge groups in supersymmetry.

Findings

Gaugino condensation for N_f ≤ 2

Instanton-generated superpotential at N_f=3

Modified and unmodified quantum moduli spaces for N_f=4 and 5

Abstract

We begin an investigation of supersymmetric theories based on exceptional groups. The flat directions are most easily parameterized using their correspondence with gauge invariant polynomials. Symmetries and holomorphy tightly constrain the superpotentials, but due to multiple gauge invariants other techniques are needed for their full determination. We give an explicit treatment of $G_2$ and find gaugino condensation for $N_f\leq 2$, and an instanton generated superpotential for $N_f=3$. The analogy with $SU(N_c)$ gauge theories continues with modified and unmodified quantum moduli spaces for $N_f=4$ and $N_f=5$ respectively, and a non-Abelian Coulomb phase for $N_f\geq6$. Electric variables suffice to describe this phase over the full range of $N_f$. The appendix gives a self-contained introduction to $G_2$ and its invariant tensors.