A relative tensor product of subfactors over a modular tensor category

2016/12/31 by Yasuyuki Kawahigashi · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebra over a field #Algebraic structures and combinatorial models #Conformal map #Fusion rules #Homotopy and Cohomology in Algebraic Topology #Product (mathematics) #Realization (probability) #Tensor (intrinsic definition) #Tensor product #Tensor product of Hilbert spaces #Tensor product of modules #math-ph #math.MP #math.OA

paper · pdf · doi:10.1007/s11005-017-0972-9

published in Letters in Mathematical Physics 107(11), 1963-1970 (Springer Science+Business Media) · 9 pages

openalex created_date 2017/01/06 · arxiv created 2017/05/15 · openalex publication_date 2017/06/02 · arxiv updated 2017/12/01 · openalex updated_date 2026/08/05

Abstract

We define and study a certain relative tensor product of subfactors over a modular tensor category. This gives a relative tensor product of two completely rational heterotic full local conformal nets with trivial superselection structures over a common chiral representation category. In particular, we have a new realization of fusion rules of modular invariants. This also gives a mathematical definition of a composition of two gapped domain walls between topological phases.

Citations

• Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy
• The Classification of Non-Local Chiral CFT with c < 1
• TFT construction of RCFT correlators I: partition functions