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 {\it globally conformal invariant} (GCI) theory we write down the OPE of $V_{\kappa}$ into a series of {\it twist} (dimension minus rank) $2\kappa$ 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 ${\cal L} (x)$ of dimension 4 in $D = 4$ Minkowski space such that the 3-point functions of a pair of ${\cal L}$'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 ${\cal L} (x)$.