Equivalence classes of boundary conditions in orbifold gauge theory

In higher-dimensional theories, the boundary conditions (BCs) along the extra dimensions play a crucial role, determining the behavior of the low-energy four-dimensional effective theory. In particular, in higher-dimensional gauge theories compactified on orbifold extra spaces, the pattern of gauge symmetry breaking depends sensitively on the choice of BCs. Although there are numerous possible choices of the BCs, some of them are related through gauge transformations and thereby form physically equivalent classes, i.e., equivalence classes. In this talk, I will first give an overview of the role of BCs in extra-dimensional models. I will then explain how BCs can be comprehensively classified by “trace conservation laws.” This talk is based on Refs. 2404.19411[hep-th] and 2501.05849[hep-th], and focuses on one- or two-dimensional orbifolds with gauge groups SU(N) or SO(N).