Unitarity of the modular tensor categories associated to unitary vertex operator algebras, I

Abstract

This is the first part in a two-part series of papers constructing a unitary structure for the modular tensor category (MTC) associated to a unitary rational vertex operator algebra (VOA).

69 pages. Abstract and introduction are revised

References in corpus (1)

• Braided tensor categories and extensions of vertex operator algebras

Cited by in corpus (16)

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• Haploid algebras in $C^{\ast }$-tensor categories and the Schellekens list
• Representation theory in chiral conformal field theory: from fields to observables
• Q-systems and extensions of completely unitary vertex operator algebras
• Energy bounds condition for intertwining operators of type $B$, $C$, and $G_2$ unitary affine vertex operator algebras
• Unitarity of the modular tensor categories associated to unitary vertex operator algebras, II
• Fusion and positivity in chiral conformal field theory
• Classification of unitary vertex subalgebras and conformal subnets for rank-one lattice chiral CFT models
• Energy bounds for vertex operator algebra extensions
• From vertex operator superalgebras to graded-local conformal nets and back
• The boundary phase transitions of the 2+1D ${\mathbb{Z}}_N$ topological order via topological Wick rotation
• 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
• Bisognano-Wichmann property for rigid categorical extensions and non-local extensions of conformal nets
• Regular vertex operator subalgebras and compressions of intertwining operators
• Polynomial energy bounds for type $F_4$ WZW-models