# Scale and Möbius covariance in two-dimensional Haag-Kastler net

July 12, 2018

Given a two-dimensional Haag-Kastler net which is Poincar\'e-dilation
covariant with additional properties, we prove that it can be extended to a
M\"obius 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 Poincar\'e-dilation covariant net which
cannot be extended to a M\"obius covariant net, and discuss the obstructions.

open access link
doi:10.1007/s00220-019-03410-x
article file

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@article{Morinelli:2018pof,
author = "Morinelli, Vincenzo and Tanimoto, Yoh",
title = "{Scale and Möbius Covariance in Two-Dimensional
Haag–Kastler Net}",
journal = "Commun. Math. Phys.",
volume = "371",
year = "2019",
number = "2",
pages = "619-650",
doi = "10.1007/s00220-019-03410-x",
eprint = "1807.04707",
archivePrefix = "arXiv",
primaryClass = "math-ph",
SLACcitation = "%%CITATION = ARXIV:1807.04707;%%"
}

Keywords:

*none*