Supersymmetric duality in superloop space

Abstract

In this paper we constructed superloop space duality for a four dimensional supersymmetric Yang-Mills theory with 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.

Topological defects in a deformed gauge theory

“…The loop space formalism has been used to construct loop space duality for ordinary Yang-Mills theories [35,36,37,38]. This duality reduces to the usual electromagnetic Hodge duality for abelian gauge theories.…”

“…Thus, we will have demonstrated that a monopole contribution can generated from deformation of loop space variables. It may be noted that monopoles in general have been analyzed in loop space using a duality which reduces to electromagnetic Hodge duality for abelian theories [35,36,37,38]. However, as far as we know, all such constructions use the loop space formalism, and we are not aware of any proof of this duality using space-time variables alone.…”

Supersymmetric Duality in Deformed Superloop Space

“…Before doing that we note that this duality reduces to an ordinary superloop space duality if we neglect the effect of noncommutativity [46]. Furthermore, for if for the non-supersymmetric case, this reduces to the ordinary loop space duality.…”

“…Furthermore, the Polyakov loops for three and four dimensional supersymmetric Yang-Mills theories with N = 1 supersymmetry have also been studied [44]- [45]. The superloop space duality has also been studied in N = 1 superspace [46]. In this paper, we will construct such superloops for deformed superspace.…”

Dualized Gravity beyond Linear Approximation

“…The problem with this approach is that it has not been possible to construct a generalization of Hodge duality to non-abelian gauge theories in spacetime. However, it is possible to construct a such a duality in Yang-Mills theories using Polyakov variable [25,23,24,26]. It has also been demonstrated that this duality reduces to the electromagnetic Hodge duality for abelian gauge theories [25].…”