Rational conformal correlation functions of gauge-invariant local fields in four dimensions

Global conformal invariance in Minkowski space and the Wightnian axioms imply strong locality (Huygens principle) and rationality of correlation functions, thus providing an extension of the concept of a vertex algebra to higher (even) dimensions D. We (p)review current work oil a model of a Hermitian scalar field L of scale dimension 4 (D = 4) which can be interpreted as the Lagrangian of a gauge field theory that generates the algebra Of gauge-invariant local observables in a conformally invariant renormalization group fixed point. (c) 2005 Pleiades Publishing, Inc.