From Vertex Operator Algebras to Conformal Nets and Back

ISBN-13: 9781470428587 / Angielski / Miękka / 2018 / 85 str.

Sebastiano Carpi; Yasuyuki Kawahigashi

Opis

Considers unitary simple vertex operator algebras whose vertex operators satisfy certain energy bounds and a strong form of locality and call them strongly local. The authors 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 $V$.

Spis treści

• Introduction;
• Preliminaries on von Neumann algebras;
• Preliminaries on conformal nets;
• Preliminaries on vertex algebras;
• Unitary vertex operator algebras;
• Energy bounds and strongly local vertex operator algebras;
• Covariant subnets and unitary subalgebras;
• Criteria for strong locality and examples;
• Back to vertex operators;
• Appendix A. Vertex algebra locality and Wightman locality;
• Appendix B. On the Bisognano-Wichmann property for representations of the Mobius group;
• Bibliography.