Superalgebras in $N=1$ Gauge Theories

TL;DR

This paper explores the structure of gauge invariant superalgebras in N=1 supersymmetric gauge theories, revealing their algebraic forms, duality interpretations, and extensions to exceptional groups like E6.

Contribution

It characterizes the superalgebras in N=1 gauge theories with various gauge groups and matter content, and proposes a duality interpretation via charge conjugation within these algebras.

Findings

Superalgebras reduce to graded Lie algebras with adjoint matter.

For SO(n_c) with vector matter, the superalgebra is a W-algebra.

The superalgebra structure extends to the E6 gauge group.

Abstract

$N=1$ supersymmetric gauge theories with global flavor symmetries contain a gauge invariant W-superalgebra which acts on its moduli space of gauge invariants. With adjoint matter, this superalgebra reduces to a graded Lie algebra. When the gauge group is $SO(n_c)$, with vector matter, it is a W-algebra, and the primary invariants form one of its representation. The same superalgebra exists in the dual theory, but its construction in terms of the dual fields suggests that duality may be understood in terms of a charge conjugation within the algebra. We extend the analysis to the gauge group $E_6$.