Communications in Mathematical Physics

, Volume 357, Issue 1, pp 379–406 | Cite as

Conformal Covariance and the Split Property

  • Vincenzo Morinelli
  • Yoh TanimotoEmail author
  • Mihály Weiner


We show that for a conformal local net of observables on the circle, the split property is automatic. Both full conformal covariance (i.e., diffeomorphism covariance) and the circle-setting play essential roles in this fact, while by previously constructed examples it was already known that even on the circle, Möbius covariance does not imply the split property.

On the other hand, here we also provide an example of a local conformal net living on the 2-dimensional Minkowski space, which—although being diffeomorphism covariant—does not have the split property.


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© The Author(s) 2017

Authors and Affiliations

  • Vincenzo Morinelli
    • 1
  • Yoh Tanimoto
    • 1
    Email author
  • Mihály Weiner
    • 2
  1. 1.Dipartimento di MatematicaUniversitá di Roma Tor VergataRomeItaly
  2. 2.Department of Analysis, Mathematical InstituteBudapest University of Technology and Economics (BME)BudapestHungary

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