Two-dimensional topological order and operator algebras

Abstract

We review recent interactions between mathematical theory of two-dimensional topological order and operator algebras, particularly the Jones theory of subfactors. The role of representation theory in terms of tensor categories is emphasized. Connections to 2-dimensional conformal field theory are also presented. In particular, we discuss anyon condensation, gapped domain walls and matrix product operators in terms of operator algebras.

review paper, 18 pages

References in corpus (3)

• Condensate induced transitions between topologically ordered phases
• A remark on gapped domain walls between topological phases
• Projector Matrix Product Operators, Anyons and Higher Relative Commutants of Subfactors

Cited by in corpus (8)

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• Quantum cellular automata and categorical dualities of spin chains
• Fusion rule in conformal field theories and topological orders: A unified view of correspondence and (fractional) supersymmetry and their relation to topological holography
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• A characterization of a finite-dimensional commuting square producing a subfactor of finite depth