Duality and Superconvergence Relation in Supersymmetric Gauge Theories

TL;DR

This paper explores the phase structures of various N=1 supersymmetric gauge theories, examining superconvergence and duality relations, and finds that Oehme's duality applies mainly to theories with fundamental matter fields.

Contribution

It extends the analysis of Oehme's duality to more general gauge theories and clarifies the conditions under which superconvergence can describe the non-Abelian Coulomb phase.

Findings

Oehme's duality holds for theories with fundamental matter fields

Superconvergence relation can describe the non-Abelian Coulomb phase

Duality does not generally extend to theories with more complex matter representations

Abstract

We investigate the phase structures of various N=1 supersymmetric gauge theories including even the exceptional gauge group from the viewpoint of superconvergence of the gauge field propagator. Especially we analyze in detail whether a new type of duality recently discovered by Oehme in $SU(N_c)$ gauge theory coupled to fundamental matter fields can be found in more general gauge theories with more general matter representations or not. The result is that in the cases of theories including matter fields in only the fundamental representation, Oehme's duality holds but otherwise it does not. In the former case, superconvergence relation might give good criterion to describe the interacting non-Abelian Coulomb phase without using some information from dual magnetic theory.