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.

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