Local conformal nets arising from framed vertex operator algebras

Abstract

We apply an idea of framed vertex operator algebras to a construction of local conformal nets of (injective type III_1) factors on the circle corresponding to various lattice vertex operator algebras and their twisted orbifolds. In particular, we give a local conformal net corresponding to the moonshine vertex operator algebras of Frenkel-Lepowsky-Meurman. Its central charge is 24, it has a trivial representation theory in the sense that the vacuum sector is the only irreducible DHR sector, its vacuum character is the modular invariant J-function and its automorphism group (the gauge group) is the Monster group. We use our previous tools such as alpha-induction and complete rationality to study extensions of local conformal nets.

24 pages; The automorphism group of the moonshine net is now identified with the monster group

References in corpus (3)

• Solitons in Affine and Permutation Orbifolds
• Conformal Orbifold Theories and Braided Crossed G-Categories
• Noncommutative Spectral Invariants and Black Hole Entropy

Cited by in corpus (32)

• From vertex operator algebras to conformal nets and back
• Conformal Field Theory, Tensor Categories and Operator Algebras
• AQFT from n-functorial QFT
• A Characetrization of Vertex Operator Algebra L(1/2,0)\otimes L(1/2,0)
• The Moonshine Anomaly
• Representations of Conformal Nets, Universal C*-Algebras and K-Theory
• Building vertex algebras from parts
• Haploid algebras in $C^{\ast }$-tensor categories and the Schellekens list
• Representation theory in chiral conformal field theory: from fields to observables
• Subfactors and Mathematical Physics
• Models in Boundary Quantum Field Theory Associated with Lattices and Loop Group Models
• W-algebra W(2,2) and the vertex operator algebra L(1/2,0)\otimes L(1/2,0)
• Conformal nets and local field theory
• Algebraic conformal quantum field theory in perspective
• A critical look at 50 years particle theory from the perspective of the crossing property
• The Ongoing Impact of Modular Localization on Particle Theory
• Causality and dispersion relations and the role of the S-matrix in the ongoing research
• Lorentzian 2d CFT from the pAQFT perspective
• Conformal Net Realizability of Tambara-Yamagami Categories and Generalized Metaplectic Modular Categories
• Massless scalar free Field in 1+1 dimensions I: Weyl algebras Products and Superselection Sectors
• Braided categories of endomorphisms as invariants for local quantum field theories
• From vertex operator superalgebras to graded-local conformal nets and back
• von Neumann Subfactors and Non-invertible Symmetries
• From Operator Algebras to Superconformal Field Theory
• The classification of chiral WZW models by $H_{+}^4(BG,\mathbb{Z})$
• Operator algebras and vertex operator algebras
• Placing hidden properties of quantum field theory into the forefront: wedge localization and a new constructive on-shell setting
• Loop groups and noncommutative geometry
• An application of Mirror extensions
• Construction of holomorphic local conformal framed nets
• Conformal Nets Associated with Lattices and Their Orbifolds
• Bicoloured torus loop groups