2-connections, a lattice point of view

TL;DR

This paper demonstrates how transition laws for 2-connections in higher gauge theory can be derived through lattice discretization, bridging continuous and discrete approaches in the field.

Contribution

It introduces a lattice-based method to recover transition laws for 2-connections, illustrating the applicability of lattice schemes in higher gauge theory.

Findings

Transition laws for 2-connections can be obtained via lattice discretization.

Lattice schemes can replicate results from continuous higher gauge theory.

The work provides a framework for discretizing 2-bundles in a hypercubic lattice.

Abstract

We show that the transition laws for a 2-connection can be recovered by discretizing the base 2-space of a 2-bundle into an Euclidean hypercubic lattice. The aim of this work is to serve as an example of how important results in higher gauge theory, which have been derived in a continuous setting, can also be derived in the lattice scheme.