Monopoles in superloop space

Abstract

In this paper, we will analyse a four dimensional gauge theory with N = 1 supersymmetry in superloop space formalism. We will thus obtain an expression for the connection in the infinite-dimensional superloop space. We will then use this connection to obtain an expression for the curvature of the infinite-dimensional superloop space. We will also show that this curvature is proportional to the Bianchi identity in spacetime. Thus, in absence of a monopole this curvature will vanish. However, it will not vanish if the superloop intersects the world-line of a monopole because the Bianchi will not hold at that point.

Supersymmetric duality in superloop space

“…The space of all such super-functions parameterizes the superloop space. A functional on this superloop space can be constructed as [35] […”

“…These superloop variables are highly redundant and have to be constrained by an infinite set of conditions which can be expressed by the vanishing of the superloop space curvature [35], …”

“…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

“…where ξ A (0) = ξ A (2π) is a fixed point on this curve [45]. We can now define the superloop variable for the deformed superspace as…”

“…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].…”