Monopoles in superloop space

¹ Department of Physics and Astronomy, University of Waterloo - Waterloo, Ontario N2L 3G1, Canada
² Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter Woodstock Road, Oxford OX2 6GG, UK

Received: 17 April 2014
Accepted: 25 June 2014

Abstract

In this paper, we will analyse a four-dimensional gauge theory with 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 the 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 identity will not hold at that point.