Monopoles in Superloop Space

TL;DR

This paper explores the geometric structure of a four-dimensional supersymmetric gauge theory in superloop space, revealing how monopoles manifest as non-vanishing curvature related to Bianchi identity violations.

Contribution

It introduces a formalism for analyzing monopoles in superloop space by deriving the connection and curvature, linking monopoles to Bianchi identity violations in supersymmetric gauge theories.

Findings

Curvature in superloop space is proportional to Bianchi identity.

Non-zero curvature indicates the presence of monopoles.

Curvature vanishes when no monopoles are present.

Abstract

In this paper, we will analyse a four dimensional gauge theory with $\mathcal{N} =1$ 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.