Generalized ADE Classification of Gapped Domain Walls

Abstract

In this paper we would like to demonstrate how the known rules of anyon condensation motivated physically proposed by Bais \textit{et al} can be recovered by the mathematics of twist-free commutative separable Frobenius algebra (CSFA). In some simple cases, those physical rules are also sufficient conditions defining a twist-free CSFA. This allows us to make use of the generalized $ADE$ classification of CSFA's and modular invariants to classify anyon condensation, and thus characterizing all gapped domain walls and gapped boundaries of a large class of topological orders. In fact, this classification is equivalent to the classification we proposed in Ref.1.

9+6 pages, 1 figure, 3 tables, minor corrections, references added

References in corpus (5)

• Non-Abelian Anyons and Topological Quantum Computation
• Generalized Global Symmetries
• Condensate induced transitions between topologically ordered phases
• A theory of topological edges and domain walls
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