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 \(V_{\kappa}(x_1,x_2)\) of dimension \((\kappa,\kappa)\). For a globally conformal invariant (GCI) theory we write down the OPE of \(V_{\kappa}\) into a series of 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 \(L(x)\) 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 \(L(x)\).


81T13 Yang-Mills and other gauge theories in quantum field theory
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
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