Supersymmetric Duality in Superloop Space

TL;DR

This paper develops a superloop space duality for 4D N=1 supersymmetric Yang-Mills theory, unifying various dualities and revealing how electric and magnetic charges interchange roles under this duality.

Contribution

It constructs a superloop space duality for 4D N=1 supersymmetric Yang-Mills theory, extending known dualities and demonstrating charge interchange.

Findings

Reduces to ordinary loop space duality for Yang-Mills.

Reduces to Hodge duality for abelian gauge theory.

Electric charges become monopoles in the dual theory.

Abstract

In this paper we constructed superloop space duality for a four dimensional supersymmetric Yang-Mills theory with $\mathcal{N} =1$ supersymmetry. This duality reduces to the ordinary loop space duality for the ordinary Yang-Mills theory. It also reduces to the Hodge duality for an abelian gauge theory. Furthermore, the electric charges, which are the sources in the original theory, appear as monopoles in the dual theory. Whereas, the magnetic charges, which appear as monopoles in the original theory, become sources in the dual theory.