From Vertex Operator Algebras to Conformal Nets and Back (Memoirs of the American Mathematical Society)

By Sebastiano Carpi

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 $\mathcal A_V$.

• Format: Paperback
• Language: English
• ISBN: 147042858X
• ISBN13: 9781470428587
• Release Date: June 2018
• Publisher: Amer Mathematical Society
• Length: 85 Pages
• Weight: 0.42 lbs.
• Dimensions: 10.3" x 0.3" x 7.3"