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Conformal Covariance and the Split Property

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Abstract

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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Authors and Affiliations

  1. Dipartimento di Matematica, Universitá di Roma Tor Vergata, Via della Ricerca Scientifica, 1, 00133, Rome, Italy

    Vincenzo Morinelli & Yoh Tanimoto

  2. Department of Analysis, Mathematical Institute, Budapest University of Technology and Economics (BME), Műegyetem rk. 3-9, Budapest, 1111, Hungary

    Mihály Weiner

Authors
  1. Vincenzo Morinelli
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  2. Yoh Tanimoto
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  3. Mihály Weiner
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Correspondence to Yoh Tanimoto.

Additional information

Communicated by D. Buchholz, K. Fredenhagen, Y. Kawahigashi

V. Morinelli: Supported by the ERC advanced Grant 669240 QUEST “Quantum Algebraic Structures and Models”.

Y. Tanimoto: Supported by the JSPS fellowship for research abroad.

M. Weiner: Supported in part by the ERC advanced Grant 669240 QUEST “Quantum Algebraic Structures and Models” and by OTKA Grant No. 104206.

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Morinelli, V., Tanimoto, Y. & Weiner, M. Conformal Covariance and the Split Property. Commun. Math. Phys. 357, 379–406 (2018). https://doi.org/10.1007/s00220-017-2961-3

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