Communications in Mathematical Physics

, Volume 322, Issue 1, pp 149–166 | Cite as

How to Add a Boundary Condition

  • Sebastiano Carpi
  • Yasuyuki Kawahigashi
  • Roberto Longo


Given a conformal QFT local net of von Neumann algebras \({\mathcal {B}_2}\) on the two-dimensional Minkowski spacetime with irreducible subnet \({\mathcal {A} \otimes \mathcal {A}}\), where \({\mathcal {A}}\) is a completely rational net on the left/right light-ray, we show how to consistently add a boundary to \({\mathcal {B}_2}\): we provide a procedure to construct a Boundary CFT net \({\mathcal {B}}\) of von Neumann algebras on the half-plane x >  0, associated with \({\mathcal {A}}\), and locally isomorphic to \({\mathcal {B}_2}\). All such locally isomorphic Boundary CFT nets arise in this way. There are only finitely many locally isomorphic Boundary CFT nets and we get them all together. In essence, we show how to directly redefine the C* representation of the restriction of \({\mathcal {B}_2}\) to the half-plane by means of subfactors and local conformal nets of von Neumann algebras on S 1.


Unitary Representation Double Cone Minkowski Plane Vacuum Vector Vacuum Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Sebastiano Carpi
    • 1
  • Yasuyuki Kawahigashi
    • 2
    • 3
  • Roberto Longo
    • 4
  1. 1.Dipartimento di EconomiaUniversità di Chieti-Pescara “G. d’Annunzio”PescaraItaly
  2. 2.Department of Mathematical SciencesThe University of TokyoKomabaJapan
  3. 3.Kavli IPMU (WPI), The University of TokyoKashiwaJapan
  4. 4.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomaItaly

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