Non-Abelian Combinatorial Gauge Theory

TL;DR

This paper extends combinatorial gauge symmetry principles to non-Abelian finite gauge groups, enabling lattice gauge theories with only one- and two-body interactions that exactly realize the symmetry.

Contribution

It generalizes the combinatorial gauge symmetry framework from Abelian to non-Abelian finite groups, broadening the scope of exact symmetry realization in lattice gauge theories.

Findings

Framework successfully extended to non-Abelian groups

Maintains exact gauge symmetry with simple interactions

Provides a basis for future non-Abelian lattice models

Abstract

Building on the principle of combinatorial gauge symmetry, lattice gauge theories can be formulated with only one- and two-body interactions that ensure the exact realization of the symmetry rather than its approximate emergence in a perturbative regime. This paper extends the framework to encompass generic non-Abelian finite gauge groups by expanding on previous work that developed the theory for finite Abelian gauge groups and presented one non-Abelian example.