Study of a lattice 2-group gauge model

TL;DR

This paper explores a lattice gauge model based on 2-groups, extending traditional gauge theories, and presents a specific realization with numerical simulations to analyze its dynamics.

Contribution

It introduces a lattice formulation of a 2-group gauge model, combining topological quantum field theory with Yang-Mills theory, and provides numerical analysis of its behavior.

Findings

Numerical results support the expected phase space dynamics.

The model successfully incorporates degrees of freedom on links and faces.

The construction offers a new approach to 2-group gauge theories.

Abstract

Gauge theories admit a generalisation in which the gauge group is replaced by a finer algebraic structure, known as a 2-group. The first model of this type is a Topological Quantum Field Theory introduced by Yetter. We discuss a common generalisation of both the Yetter's model and Yang-Mills theory and in particular we focus on the lattice formulation of such model for finite 2-groups. In the second part we present a particular realization based on a 2-group constructed from $\mathbb Z_4$ groups. In the selected model, independent degrees of freedom are associated to both links and faces of a four-dimensional lattice and are subject to a certain constraint. We present the details of this construction, discuss the expected dynamics in different regions of phase space and show numerical results from Monte Carlo simulations corroborating these expectations.