Conformal Haag-Kastler nets, pointlike localized fields and the existence of operator product expansions

Starting from a chiral conformal Haag-Kastler net on 2 dimensional Minkowski space we construct associated pointlike localized fields. This amounts to a proof of the existence of operator product expansions.We derive the result in two ways. One is based on the geometrical identification of the modular structure, the other depends on a “conformal cluster theorem” of the conformal two-point-functions in algebraic quantum field theory.The existence of the fields then implies important structural properties of the theory, as PCT-invariance, the Bisognano-Wichmann identification of modular operators, Haag duality and additivity