Supersymmetric Duality in Deformed Superloop Space

TL;DR

This paper explores the effects of non-anticommutative deformation on supersymmetric Yang-Mills theory in four dimensions, analyzing how superloop space duality relates sources and monopoles under this deformation.

Contribution

It introduces a formalism for superloop space duality in deformed $ ext{N}=1/2$ supersymmetric Yang-Mills theory, revealing the duality between sources and monopoles.

Findings

Sources become monopoles in the dual theory

Monopoles become sources in the dual theory

Deformation breaks half the supersymmetry

Abstract

In this paper, we will analyse the superloop space formalism for a four dimensional supersymmetric Yang-Mills theory in deformed superspace. We will deform the $\mathcal{N} =1$ superspace by imposing non-anticommutativity. This non-anticommutative deformation of the superspace will break half the supersymmetry of the original theory. So, this theory will have $\mathcal{N} =1/2$ supersymmetry. We will analyse the superloop space duality for this deformed supersymmetric Yang-Mills theory using the $\mathcal{N} =1/2$ superspace formalism. We will demonstrate that the sources in the original theory will become monopoles in the dual theory, and the monopoles in the original theory will become sources in the dual theory.