Scale and Möbius Covariance in Two-Dimensional Haag–Kastler Net

  • Vincenzo Morinelli
  • Yoh TanimotoEmail author


Given a two-dimensional Haag–Kastler net which is Poincaré-dilation covariant with additional properties, we prove that it can be extended to a Möbius covariant net. Additional properties are either a certain condition on modular covariance, or a variant of strong additivity. The proof relies neither on the existence of stress-energy tensor nor any assumption on scaling dimensions. We exhibit some examples of Poincaré-dilation covariant net which cannot be extended to a Möbius covariant net, and discuss the obstructions.


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We thank Yu Nakayama for interesting discussions and bibliographical information. The authors acknowledge the MIUR Excellence Department Project awarded to the Department of Mathematics, University of Rome Tor Vergata, CUP E83C18000100006.


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© The Author(s) 2019

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di Roma Tor VergataRomaItaly

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