Spectroscopy of Gauge Theories Based on Exceptional Lie Groups

Abstract

We generate by computer a basis of invariants for the fundamental representations of the exceptional Lie groups E(6) and E(7), up to degree 18. We discuss the relevance of this calculation for the study of supersymmetric gauge theories, and revisit the self-dual exceptional models. We study the chiral ring of G(2) to degree 13, as well as a few classical groups. The homological dimension of a ring is a natural estimator of its complexity and provides a guideline for identifying theories that have a good chance to be amenable to a solution.

36 pages, no figures; version 2: 3 footnotes and 3 references added

References in corpus (2)

• Geometric invariant theory approach to the determination of ground states of D-wave condensates in isotropic space
• Supersymmetric Flat Directions and Analytic Gauge Invariants

Cited by in corpus (5)

• Elliptic hypergeometry of supersymmetric dualities
• Superconformal indices of $\mathcal{N}=4$ SYM field theories
• "Chiral'' and "Non-chiral'' 3d Seiberg duality
• 3d exceptional gauge theories and boundary confinement
• Confinement in 3d $\mathcal{N}=2$ exceptional gauge theories