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From Vertex Operator Algebras to Conformal Nets and Back
 
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
From Vertex Operator Algebras to Conformal Nets and Back
Softcover ISBN:  978-1-4704-2858-7
Product Code:  MEMO/254/1213
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
eBook ISBN:  978-1-4704-4742-7
Product Code:  MEMO/254/1213.E
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
Softcover ISBN:  978-1-4704-2858-7
eBook: ISBN:  978-1-4704-4742-7
Product Code:  MEMO/254/1213.B
List Price: $156.00 $117.00
MAA Member Price: $140.40 $105.30
AMS Member Price: $93.60 $70.20
From Vertex Operator Algebras to Conformal Nets and Back
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From Vertex Operator Algebras to Conformal Nets and Back
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
Softcover ISBN:  978-1-4704-2858-7
Product Code:  MEMO/254/1213
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
eBook ISBN:  978-1-4704-4742-7
Product Code:  MEMO/254/1213.E
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
Softcover ISBN:  978-1-4704-2858-7
eBook ISBN:  978-1-4704-4742-7
Product Code:  MEMO/254/1213.B
List Price: $156.00 $117.00
MAA Member Price: $140.40 $105.30
AMS Member Price: $93.60 $70.20
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2542018; 85 pp
    MSC: Primary 17; 46; 81

    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 \(\mathcal A_V\).

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Preliminaries on von Neumann algebras
    • 3. Preliminaries on conformal nets
    • 4. Preliminaries on vertex algebras
    • 5. Unitary vertex operator algebras
    • 6. Energy bounds and strongly local vertex operator algebras
    • 7. Covariant subnets and unitary subalgebras
    • 8. Criteria for strong locality and examples
    • 9. Back to vertex operators
    • A. Vertex algebra locality and Wightman locality
    • B. On the Bisognano-Wichmann property for representations of the Mobius̈ group
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2542018; 85 pp
MSC: Primary 17; 46; 81

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 \(\mathcal A_V\).

  • Chapters
  • 1. Introduction
  • 2. Preliminaries on von Neumann algebras
  • 3. Preliminaries on conformal nets
  • 4. Preliminaries on vertex algebras
  • 5. Unitary vertex operator algebras
  • 6. Energy bounds and strongly local vertex operator algebras
  • 7. Covariant subnets and unitary subalgebras
  • 8. Criteria for strong locality and examples
  • 9. Back to vertex operators
  • A. Vertex algebra locality and Wightman locality
  • B. On the Bisognano-Wichmann property for representations of the Mobius̈ group
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.