Globally conformal invariant gauge field theory with rational correlation functions

Details Globally conformal invariant gauge field theory with rational correlation functions Globally conformal invariant gauge field theory with rational correlation functions

2003-05-22

arxiv.org/abs/hep-th/0305200v2

Nucl.Phys. B670 (2003) 373-400

Physics

High Energy Physics

High Energy Physics - Theory

32 pages, LATEX, amssymb

Scientific paper

10.1016/j.nuclphysb.2003.08.006

Operator product expansions (OPE) for the product of a scalar field with its conjugate are presented as infinite sums of bilocal fields V_k (x_1, x_2) of dimension (k,k). For a {\it globally conformal invariant} (GCI) theory we write down the OPE of V_k into a series of {\it twist} (dimension minus rank) 2k 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).

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