Globally conformal invariant gauge field theory with rational correlation functions

Operator product expansions (OPE) for the product of a scalar field with its conjugate are presented as infinite sums of bilocal fields V-kappa(x(1), x(2)) of dimension (kappa, kappa). For a globally conformal invariant (GCI) theory we write down the OPE of VK into a series of twist (dimension minus rank) 2kappa symmetric traceless tensor fields with coefficients computed from the (rational) 4-point function of the scalar field. We argue that the theory of a GCI hermitian scalar field L(x) of dimension 4 in D = 4 Minkowski space such that the 3-point functions of a pair of L's and a scalar field of dimension 2 or 4 vanish can be interpreted as the theory of local observables of a conformally invariant fixed point in a gauge theory with Lagrangian density L(x). (C) 2003 Elsevier B.V. All rights reserved.