Supersymmetric Gauge Theories with an Affine Quantum Moduli Space

TL;DR

This paper classifies supersymmetric gauge theories with affine quantum moduli spaces, identifying unique theories with no gauge invariants and establishing conditions on matter representations for theories with relations among invariants.

Contribution

It provides a complete classification of simple group supersymmetric gauge theories with affine quantum moduli spaces, including the unique theories with a single point moduli space.

Findings

Only two theories have no gauge invariants: SU(5) with 5-bar + 10 and SO(10) with a spinor.

The index of matter representations must be at least that of the adjoint for theories with relations among invariants.

The paper confirms the structure of moduli spaces for classified theories.

Abstract

All supersymmetric gauge theories based on simple groups which have an affine quantum moduli space, i.e. one generated by gauge invariants with no relations, W=0, and anomaly matching at the origin, are classified. It is shown that the only theories with no gauge invariants (and moduli space equal to a single point) are the two known examples, SU(5) with 5-bar + 10 and SO(10) with a spinor. The index of the matter representation must be at least as big as the index of the adjoint in theories which have a non-trivial relation among the gauge invariants.