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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 ${V}_{\kappa }\left({x}_{1},{x}_{2}\right)$ of dimension $\left(\kappa ,\kappa \right)$. 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 $L\left(x\right)$ 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 $L\left(x\right)$.
##### MSC:
 81T13 Yang-Mills and other gauge theories 81T40 Two-dimensional field theories, conformal field theories, etc.