Parallel transport on non-Abelian flux tubes

TL;DR

This paper introduces a gauge-theoretic framework for unambiguous parallel transport on non-Abelian flux tubes using two gauge fields, leading to a Lie 2-group structure and effective actions for two-form fields.

Contribution

It presents a novel method for parallel transporting fields on non-Abelian flux tubes with an integrability condition, resulting in a gauge theory based on Lie 2-groups.

Findings

Unambiguous parallel transport on non-Abelian flux tubes achieved.

Integrability condition ensures consistency of parallel transport.

Effective actions for two-form fields derived from the framework.

Abstract

I propose a way of unambiguously parallel transporting fields on non-Abelian flux tubes, or strings, by means of two gauge fields. One gauge field transports along the tube, while the other transports normal to the tube. Ambiguity is removed by imposing an integrability condition on the pair of fields. The construction leads to a gauge theory of mathematical objects known as Lie 2-groups, which are known to result also from the parallel transport of the flux tubes themselves. The integrability condition is also shown to be equivalent to the assumption that parallel transport along nearby string configurations are equal up to arbitrary gauge transformations. Attempts to implement this condition in a field theory leads to effective actions for two-form fields.