Some exact results in supersymmetric theories based on exceptional groups

Details Some exact results in supersymmetric theories based on exceptional groups Some exact results in supersymmetric theories based on exceptional groups

1995-06-30

arxiv.org/abs/hep-th/9506196v1

Phys.Rev. D52 (1995) 6065-6073

Physics

High Energy Physics

High Energy Physics - Theory

27 pages (harvmac l mode)

Scientific paper

10.1103/PhysRevD.52.6065

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.

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