Path space forms and surface holonomy

TL;DR

This paper develops a differential geometric approach to parallel transport on path spaces, linking it with category theory, and advances higher gauge theory through 2-connections where endpoints are flexible.

Contribution

It introduces a new geometric method for path space parallel transport that integrates with higher gauge theory and 2-connections, expanding the scope of gauge theories.

Findings

Connects differential geometric and category theoretic approaches

Advances higher gauge theory with flexible endpoint 2-connections

Provides a framework for parallel transport on path spaces

Abstract

We develop parallel transport on path spaces from a differential geometric approach, whose integral version connects with the category theoretic approach. In the framework of 2-connections, our approach leads to further development of higher gauge theory, where end points of the path need not be fixed.