New Classification Method for Equivalence Classes on S1/Z2 and T2/Z3 Orbifolds

Abstract In 5D and 6D U(N) and SU(N) gauge theories compactified on S1/Z2 and T2/Z3 orbifolds, we propose a new method to classify the equivalence classes (ECs) of boundary conditions (BCs) without depending on the structure of gauge transformations. Some of the BCs are connected through gauge transformations and constitute ECs, each of which contains physically equivalent BCs. Previous methods for classifying ECs have been used for specific gauge transformations. In this paper, we show that a geometric property of orbifolds significantly narrows down the possibilities of connecting BCs and completes the classification of ECs.