Supersymmetric Duality in Deformed Superloop Space

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 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 N = 1/2 supersymmetry. We will analyse the superloop space duality for this deformed supersymmetric Yang-Mills theory using the 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.

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.…”

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].…”

“…The connection in the Polyakov loop space is called Polyakov variable. As this Polyakov variable which has been used to construct a nonabelian generalization of Hodge duality [25,23,24,26], and gravity can be constructed as a gauge theory of Lorentz group [17,18,19,20,21,22], we can construct Polyakov variable for gravity, and use it to construct a dual for gravity beyond linearized approximation. It may be noted that this duality has been used in Yang-Mills theories to obtain several interesting results.…”

“…This supersymmetric loop space has also been used to construct a dual potential in supersymmetric gauge theories [23]. This has been generalized to a deformed supersymmetric gauge theory using deformed superspace [24]. Polyakov loops space has also been used for investigating the topological defects in fractional M2-branes [8].…”