A new formulation of higher parallel transport in higher gauge theory
Emanuele Soncini, Roberto Zucchini
TL;DR
This paper introduces a novel mathematical framework for higher parallel transport in higher gauge theory, crucial for defining Wilson lines and surfaces, using Lie crossed module cocycles and a double category perspective.
Contribution
It presents a new formulation of higher parallel transport based on Lie crossed module cocycles and a double category approach, establishing equivalence with previous models.
Findings
New formulation of higher parallel transport using Lie crossed modules
Double category interpretation of gauge transformations
Equivalence to earlier higher gauge theory formulations
Abstract
In this technical paper, we present a new formulation of higher parallel transport in strict higher gauge theory required for the rigorous construction of Wilson lines and surfaces. Our approach is based on an original notion of Lie crossed module cocycle and cocycle 1- and 2-gauge transformation with a non standard double category theoretic interpretation. We show its equivalence to earlier formulations.
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