Mixed symmetry Wilson-loop interactions in the worldline formalism

TL;DR

This paper develops a worldline formalism approach to describe matter fields in arbitrary gauge group representations, enabling accurate computation of Wilson-loop interactions and broadening applications in gauge theory observables.

Contribution

It introduces a method to incorporate matter fields in any representation within the worldline formalism, overcoming previous limitations and enabling more general calculations.

Findings

Successfully projects onto arbitrary irreducible representations

Accurately reproduces Wilson-loop interactions for matter fields

Extends the applicability of worldline techniques to new matter types

Abstract

Using the worldline formalism of the Dirac field with a non-Abelian gauge symmetry we show how to describe the matter field transforming in an arbitrary representation of the gauge group. Colour degrees of freedom are carried on the worldline by auxiliary fields, responsible for providing path ordering and the Wilson-loop coupling. The Hilbert space of these fields is reducible but we make use of recent work in order to project onto a single, arbitrary, irreducible representation. By functionally quantising the resulting theory we show that this procedure correctly generates the Wilson-loop interaction between the gauge field and the matter field taken to transform in a chosen representation. This work has direct application to physical observables such as scattering amplitudes in the presence of such a matter multiplet and lifts the restriction on the type of matter that has previously featured in worldline calculations.