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Globally conformal invariant gauge field theory with rational correlation functions. (English) Zbl 1058.81054
Summary: Operator product expansions (OPE) for the product of a scalar field with its conjugate are presented as infinite sums of bilocal fields V κ (x 1 ,x 2 ) of dimension (κ,κ). For a globally conformal invariant (GCI) theory we write down the OPE of V κ into a series of twist (dimension minus rank) 2κ 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).
81T13Yang-Mills and other gauge theories
81T40Two-dimensional field theories, conformal field theories, etc.