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Zbl 1058.81054
Nikolov, N.M.; Stanev, Ya.S.; Todorov, I.T.
Globally conformal invariant gauge field theory with rational correlation functions. (English)
[J] Nucl. Phys., B 670, No. 3, 373-400 (2003). ISSN 0550-3213

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 $L(x)$.

MSC 2000:: *81T13 Gauge theories
81T40 Two-dimensional field theories, etc.

Keywords: operator product expansions; symmetric traceless tensor fields; sclar-field 4-point function

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