Globally conformal invariant gauge field theory with rational correlation functions

2003/05/31 by Nikolay M. Nikolov, Yassen S. Stanev, Ivan T. Todorov
Physics and Astronomy · #hep-th

paper · pdf · doi:10.1016/j.nuclphysb.2003.08.006

published as Nucl.Phys. B670 (2003) 373-400 · 32 pages, LATEX, amssymb

arxiv created 2003/07/05 · arxiv updated 2009/11/30

Abstract

Operator product expansions (OPE) for the product of a scalar field with its conjugate are presented as infinite sums of bilocal fields V_k (x₁, x₂) 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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