From Vertex Operator Algebras to Conformal Nets and Back
Aug 2018 · American Mathematical Soc.
Ebook
85
Pages
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About this ebook
The authors consider unitary simple vertex operator algebras whose vertex operators satisfy certain energy bounds and a strong form of locality and call them strongly local. They present a general procedure which associates to every strongly local vertex operator algebra V a conformal net AV acting on the Hilbert space completion of V and prove that the isomorphism class of AV does not depend on the choice of the scalar product on V. They show that the class of strongly local vertex operator algebras is closed under taking tensor products and unitary subalgebras and that, for every strongly local vertex operator algebra V, the map W↦AW gives a one-to-one correspondence between the unitary subalgebras W of V and the covariant subnets of AV.
About the author
Sebastiano Carpi: Università di Chieti-Pescara "G. d’Annunzio", Pescara, Italy,
Yasuyuki Kawahigashi: University of Tokyo, Tokyo, Japan,
Roberto Longo: Università di Roma "Tor Vergata", Roma, Italy,
Mihály Weiner: Budapest University of Technology and Economics, Budapest, Hungary
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