Equivalence of effective superpotentials

TL;DR

This paper demonstrates that the low-energy effective superpotential of an N=1 U(N) gauge theory with adjoint matter and a specific superpotential is equivalent in form to that of a fundamental matter theory, after rescaling couplings.

Contribution

It establishes a functional equivalence between effective superpotentials of different matter representations in N=1 gauge theories, extending previous understanding.

Findings

Effective superpotentials share the same functional form after rescaling.

The equivalence holds in the classically unbroken case.

The reasoning can be applied to other gauge theory scenarios.

Abstract

We show that the low-energy effective superpotential of an N=1 U(N) gauge theory with matter in the adjoint and arbitrary even tree-level superpotential has, in the classically unbroken case, the same functional form as the effective superpotential of a U(N) gauge theory with matter in the fundamental and the same tree-level interactions, up to some rescalings of the couplings. We also argue that the same kind of reasoning can be applied to other cases as well.