Excitations in the Higher Lattice Gauge Theory Model for Topological Phases III: the (3+1)-Dimensional Case

TL;DR

This paper extends the higher lattice gauge theory model for topological phases to 3+1 dimensions, explicitly constructing operators for excitations, analyzing their braiding, and understanding condensation and confinement phenomena.

Contribution

It provides the first detailed construction of ribbon and membrane operators in 3+1D, revealing new topological excitation behaviors and measurement techniques.

Findings

Explicit construction of ribbon and membrane operators in 3+1D

Identification of braiding relations among excitations

Analysis of condensation and confinement patterns

Abstract

In this, the third paper in our series describing the excitations of the higher lattice gauge theory model for topological phases, we will examine the 3+1d case in detail. We will explicitly construct the ribbon and membrane operators which create the topological excitations, and use these creation operators to find the pattern of condensation and confinement. We also use these operators to find the braiding relations of the excitations, and to construct charge measurement operators which project to states of definite topological charge.