Unbounded field operators in categorical extensions of conformal nets

Abstract

We prove the equivalence of VOA tensor categories and conformal net tensor categories for the following examples: all WZW models; all lattice VOAs; all unitary parafermion VOAs; type $ADE$ discrete series $W$-algebras; their tensor products; their regular cosets. A new proof of the complete rationality of conformal nets is also given.

65 pages. Final revision. Significant renumbering of sections, theorems, and equations to match the published version. Published in Invent. Math

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• Tensor categories for vertex operator superalgebra extensions
• Conformal Subnets and Intermediate Subfactors
• On the tensor structure of modules for compact orbifold vertex operator algebras
• Categorical extensions of conformal nets
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Cited by in corpus (5)

• Two-dimensional topological order and operator algebras
• Local energy bounds and strong locality in chiral CFT
• Energy bounds for vertex operator algebra extensions
• Unitarity and strong graded locality of holomorphic vertex operator superalgebras with central charge at most 24
• Regular vertex operator subalgebras and compressions of intertwining operators