From Vertex Operator Algebras to Conformal Nets and Back
We consider unitary simple vertex operator algebras whose vertex operators satisfy certain energy bounds and a strong form of locality and call them strongly local. We present a general procedure which associates to every strongly local vertex operator algebra
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| Main Authors: | , , , |
|---|---|
| Format: | eBook Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
2018
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| Edition: | 1 |
| Series: | Memoirs of the American Mathematical Society |
| Subjects: | |
| ISBN: | 147042858X, 9781470428587 |
| ISSN: | 0065-9266, 1947-6221 |
| Online Access: | Get full text |
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Table of Contents:
- 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 -- Vertex algebra locality and Wightman locality -- On the Bisognano-Wichmann property for representations of the Mobius̈ group
- Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Preliminaries on von Neumann algebras -- 2.1. Von Neumann algebras -- 2.2. Unbounded operators affiliated with von Neumann algebras -- 2.3. Tomita-Takesaki modular theory -- Chapter 3. Preliminaries on conformal nets -- 3.1. \diff and its subgroup \mob -- 3.2. Positive-energy projective unitary representations of \diff and of \difftilde and positive-energy representations of -- 3.3. Möbius covariant nets and conformal nets on \s1 -- 3.4. Covariant subnets -- Chapter 4. Preliminaries on vertex algebras -- 4.1. Vertex algebras -- 4.2. Conformal vertex algebras -- 4.3. Vertex operator algebras and invariant bilinear forms -- Chapter 5. Unitary vertex operator algebras -- 5.1. Definition of unitarity -- 5.2. An equivalent approach to unitarity -- 5.3. Unitary automorphisms and essential uniqueness of the unitary structure -- 5.4. Unitary subalgebras -- Chapter 6. Energy bounds and strongly local vertex operator algebras -- Chapter 7. Covariant subnets and unitary subalgebras -- Chapter 8. Criteria for strong locality and examples -- Chapter 9. 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 -- Acknowledgments -- Bibliography -- Back Cover