Fusing Binary Interface Defects in Topological Phases: The Vec⁡(Z/pZ)\operatorname{Vec}(\mathbb{Z}/p\mathbb{Z}) case

A binary interface defect is any interface between two (not necessarily invertible) domain walls. We compute all possible binary interface defects in Kitaev's $\mathbb{Z}/p\mathbb{Z}$ model and all possible fusions between them. Our methods can be applied to any Levin-Wen model. We also give physical interpretations for each of the defects in the $\mathbb{Z}/p\mathbb{Z}$ model. These physical interpretations provide a new graphical calculus which can be used to compute defect fusion.Comment: 27+10 pages, 2+5 tables, comments welcom