On higher holonomy invariants in higher gauge theory I

TL;DR

This paper introduces the concept of 2-holonomy for surface knots in higher gauge theory, analyzing its properties and transformations, with applications to higher Chern–Simons theory.

Contribution

It defines 2-holonomy for flat 2-connections and studies its covariance properties under gauge transformations and base changes.

Findings

Defined 2-holonomy for surface knots of arbitrary genus

Analyzed covariance under gauge transformations

Applied results to higher Chern–Simons theory

Abstract

This is the first of a series of two technical papers devoted to the analysis of holonomy invariants in strict higher gauge theory with end applications in higher Chern--Simons theory. For a flat 2--connection, we define the 2-holonomy of surface knots of arbitrary genus and determine its covariance properties under 1--gauge transformation and change of base data.