Superloop space

Abstract

In this paper will construct and analyse the superloop space formulation of a N = 1 supergauge theory in three dimensions. We will obtain expressions for the connection and the curvature in this superloop space in terms of ordinary supergauge fields. This curvature will vanish, unless there is a monopole in the spacetime. We will also construct a quantity which will give the monopole charge in this formalism. Finally, we will show how these results even hold for a deformed superspace.

Supersymmetric duality in superloop space

“…This would also occur if we were constructing superloop space in higher dimensions. Furthermore, it has been demonstrated that three dimensional superloop space requires a small number of Grassmann coordinates [34]. The superloop can now be parameterized by…”

“…It may be noted that Wilsons loops for super-Yang-Mills theory with N = 4 supersymmetry has also been constructed in superspace formalism [33]. The Polyakov loops for three and four dimensional supersymmetric Yang-Mills theories with N = 1 supersymmetry have also been studied [34,35]. In this paper we will derive a supersymmetric duality for the four dimensional supersymmetric Yang-Mills theory in the Wess-Zumino gauge.…”

Supersymmetric Duality in Deformed Superloop Space

“…The Wilsons loops for super-Yang-Mills theory with N = 4 supersymmetry has been analysed using the superspace formalism [43]. 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].…”

Monopoles in superloop space

“…Polyakov loop space has been generalized to N = 1 superloop space in three dimensions [5]. It is interesting to further generalize this to N = 1 superloop space in four dimensions, because then it can be used to study various important physical systems.…”