Categorical extensions of conformal nets

Abstract

An important goal in studying the relations between unitary VOAs and conformal nets is to prove the equivalence of their ribbon categories. In this article, we prove this conjecture for many familiar examples. Our main idea is to construct new structures associated to conformal nets: the categorical extensions.

80 pages, to appear in Commun. Math. Phys

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Cited by in corpus (16)

• Haploid algebras in $C^{\ast }$-tensor categories and the Schellekens list
• Q-systems and extensions of completely unitary vertex operator algebras
• Local energy bounds and strong locality in chiral CFT
• Fusion and positivity in chiral conformal field theory
• Unbounded field operators in categorical extensions of conformal nets
• Wightman fields for two-dimensional conformal field theories with pointed representation category
• Energy bounds for vertex operator algebra extensions
• From vertex operator superalgebras to graded-local conformal nets and back
• Geometric Positivity of the Fusion Products of Unitary Vertex Operator Algebra Modules
• Unitarity and strong graded locality of holomorphic vertex operator superalgebras with central charge at most 24
• Non-unitary Wightman CFTs and non-unitary vertex algebras
• Bisognano-Wichmann property for rigid categorical extensions and non-local extensions of conformal nets
• Regular vertex operator subalgebras and compressions of intertwining operators
• On a Connes Fusion Approach to Finite Index Extensions of Conformal Nets
• Unitary coboundary weak quasi-Hopf algebras in the Kazhdan-Lusztig-Finkelberg theorem
• Genus-zero Permutation-twisted Conformal Blocks for Tensor Product Vertex Operator Algebras: The Tensor-factorizable Case