Adjusted Parallel Transport for Higher Gauge Theories

TL;DR

This paper introduces a generalized notion of higher gauge connections that removes the fake flatness constraint, enabling truly non-abelian parallel transport in higher gauge theories like string theory.

Contribution

It defines a new higher holonomy functor that allows non-abelian higher gauge fields without the fake flatness restriction, advancing the mathematical framework of higher gauge theories.

Findings

Developed a generalized higher holonomy functor

Enabled non-abelian parallel transport in higher gauge theories

Overcame limitations of previous fake flatness condition

Abstract

Many physical theories, including notably string theory, require non-abelian higher gauge fields defining higher holonomy. Previous approaches to such higher connections on categorified principal bundles require these to be fake flat. This condition, however, renders them locally gauge equivalent to connections on abelian gerbes. For particular higher gauge groups, for example 2-group models of the string group, this limitation can be overcome by generalizing the notion of higher connection. Starting from this observation, we define a corresponding generalized higher holonomy functor which is free from the fake flatness condition, leading to a truly non-abelian parallel transport.