Mandelstam formulae for generalised Wilson loops

TL;DR

This paper derives Mandelstam formulae for generalized Wilson loops, replacing path-ordering with an anti-commuting field theory and extending to super-Wilson loops with supersymmetry.

Contribution

It introduces a novel approach to Wilson loops using anti-commuting fields and extends the formalism to include N=1 super-Wilson loops.

Findings

Derived Mandelstam formulae for generalized Wilson loops.

Replaced path-ordering with an anti-commuting field theory.

Extended the formalism to N=1 super-Wilson loops.

Abstract

We derive Mandelstam formulae for two generalisations of the Wilson loop. In these generalisations path-ordering of Lie algebra generators is replaced by an anti-commuting one dimensional field theory along the loop. We extend the calculation to the N=1 super-Wilson loop by introducing a superpartner for the additional field.