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

Abstract

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.

27+10 pages, 2+5 tables, comments welcome

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• Codimension-2 defects and higher symmetries in (3+1)D topological phases
• Composing topological domain walls and anyon mobility
• Computing data for Levin-Wen with defects
• Domain walls in topological phases and the Brauer-Picard ring for $\mathrm{Vec}(\mathbb{Z}/p\mathbb{Z})$
• Computing associators of endomorphism fusion categories
• Invertible bimodule categories and generalized Schur orthogonality
• Extend The Levin-Wen Model To Two-dimensional Topological Orders With Gapped Boundary Junctions
• Bulk-to-boundary anyon fusion from microscopic models
• Computing Defects Associated to Bounded Domain Wall Structures: The $\mathrm{Vec}(\mathbb{Z}/p\mathbb{Z})$ Case
• Equivalences of Graded Categories
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
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