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

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.

arXiv comment35 pages, 9 Tikz figures. See http://www.mat.uniroma2.it/~tanimoto/smc18.pdf for figures with better fading

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• The Bisognano-Wichmann property for asymptotically complete massless QFT
• Wightman fields for two-dimensional conformal field theories with pointed representation category
• Spacelike deformations: Higher-helicity fields from scalar fields
• Ground state representations of some non-rational conformal nets
• Scale without Conformal Invariance in bottom-up Holography