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

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Abstract

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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Acknowledgements

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

    Vincenzo Morinelli & Yoh Tanimoto

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  1. Vincenzo Morinelli
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Correspondence to Yoh Tanimoto.

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Communicated by Y. Kawahigashi

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V. Morinelli: Supported in part by the ERC Advanced Grant 669240 QUEST “Quantum Algebraic Structures and Models”, MIUR FARE R16X5RB55W QUEST-NET, GNAMPA-INdAM.

Y. Tanimoto: Supported by Programma per giovani ricercatori, anno 2014 “Rita Levi Montalcini” of the Italian Ministry of Education, University and Research.

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Morinelli, V., Tanimoto, Y. Scale and Möbius Covariance in Two-Dimensional Haag–Kastler Net. Commun. Math. Phys. 371, 619–650 (2019). https://doi.org/10.1007/s00220-019-03410-x

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