Higher lattice gauge theory from representations of 2-groups and 3+1D topological phases

TL;DR

This paper develops a higher lattice gauge theory using 2-group representations, leading to an exactly solvable model for 3+1D topological phases with topological ground states.

Contribution

It introduces a novel higher lattice gauge theory framework based on 2-group representations, enabling the construction of a solvable Hamiltonian for 3+1D topological phases.

Findings

Constructed a higher lattice gauge theory from 2-group representations.

Developed an exactly solvable Hamiltonian for 3+1D topological phases.

Identified topological ground states as observables.

Abstract

We construct a higher lattice gauge theory based on the representation of 2-groups described by a category of crossed modules on a lattice model described by path 2-groupoids. Using these lattice gauge representations, an exactly solvable Hamiltonian for topological phases in 3+1 dimensions is constructed. We show that the ground states of this model are topological observables.