Violation of the Locality condition in CFT2

Ebrahimi-Fard, Kurusch and von Rummell, Nicolai (2001) Violation of the Locality condition in CFT2.

Abstract

We present some recent results concerning the
identification of the modular structure of von Neumann algebras with spacetime symmetries within the framework of the algebraic formulation of conformal quantum field theory in 2 dimensions. We discuss the localization properties of a new class of KMS-states invariant under representations of the Moebius group generated by higher modes of the Virasoro algebra and show that the usual formulation of locality within the algebraic approach fails in this setting. This can either be circumvented by modifying the
notion of spacelike separation or by starting out with
multilocalized von Neumann algebras. We argue that this violation of the locality condition is closely connected to the KMS-states not being faithful on the algebra.