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From Vertex Operator Algebras to Conformal Nets and Back

Memoirs of the American Mathematical Society

Format: Paperback / softback
Publisher: American Mathematical Society, Providence, United States
Published: 30th Jul 2018
Dimensions: w 178mm h 254mm d 20mm
Weight: 189g
ISBN-10: 147042858X
ISBN-13: 9781470428587
Barcode No: 9781470428587
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Synopsis
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 $\mathcal A_V$ acting on the Hilbert space completion of $V$ and prove that the isomorphism class of $\mathcal A_V$ 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 $W\mapsto \mathcal A_W$ gives a one-to-one correspondence between the unitary subalgebras $W$ of $V$ and the covariant subnets of $\mathcal A_V$.

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