Superloop Space

TL;DR

This paper develops a superloop space formulation for three-dimensional $ abla=1$ supergauge theories, linking supergauge fields to superloop space connections and curvatures, and introduces a monopole charge detector that remains valid even in deformed superspaces.

Contribution

It introduces a superloop space framework for supergauge theories, connecting supergauge fields with superloop space structures and monopole charge detection, including in deformed superspaces.

Findings

Curvature in superloop space vanishes unless monopoles are present.

A new quantity for monopole charge in superloop space is constructed.

Results hold even in deformed superspace settings.

Abstract

In this paper will construct and analyse the superloop space formulation of a $\mathcal{N} =1$ 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.