Spectroscopy of Gauge Theories Based on Exceptional Lie Groups

TL;DR

This paper computes invariants for exceptional Lie groups E(6) and E(7), exploring their relevance in supersymmetric gauge theories and analyzing the complexity of related algebraic structures.

Contribution

It provides a computational basis of invariants for E(6) and E(7), and investigates their implications in gauge theory models and algebraic complexity.

Findings

Generated invariants up to degree 18 for E(6) and E(7)

Analyzed the chiral ring of G(2) up to degree 13

Discussed the complexity of gauge theories via homological dimension

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.