Equivalence Classes of Boundary Conditions in SU(N) Gauge Theory on 2-dimensional Orbifolds

TL;DR

This paper classifies boundary condition equivalence classes in SU(N) gauge theories on various 2D orbifolds, providing a systematic understanding of gauge boundary conditions in higher-dimensional models.

Contribution

It introduces a comprehensive classification of boundary conditions and their equivalence relations for SU(N) gauge theories on multiple 2D orbifolds, expanding the understanding of gauge boundary conditions.

Findings

Derived gauge transformation properties for orbifold boundary conditions.

Established equivalence relations among boundary conditions.

Classified boundary conditions related to diagonal representatives.

Abstract

We study equivalence classes of boundary conditions in an SU(N) gauge theory on six-dimensional space-time including two-dimensional orbifold. For five kinds of two-dimensional orbifolds $S^1/Z_2 \times S^1/Z_2$ and $T^2/Z_m$ $(m=2,3,4,6)$, orbifold conditions and those gauge transformation properties are given and the equivalence relations among boundary conditions are derived. The classification of boundary conditions related to diagonal representatives is carried out using the equivalence relations.