Rationality of conformally invariant local correlation functions on compactified Minkowski space

Rationality of the Wightman functions is proven to follow from energy posit ivity, locality and a natural condition of global conformal invariance (GCI ) in any number D of space-time dimensions. The GCI condition allows to tre at correlation functions as generalized sections of a vector bundle over th e compactification (M) over bar of Minkowski space M and yields a strong fo rm of locality valid for all non-isotropic intervals if assumed true for sp ace-like separations.