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Harmonic bilocal fields generated by globally conformal invariant scalar fields. (English) Zbl 1144.81028
Summary: The twist two contribution in the operator product expansion of ϕ 1 (x 1 )ϕ 2 (x 2 ) for a pair of globally conformal invariant, scalar fields of equal scaling dimension d in four space-time dimensions is a field V 1 (x 1 ,x 2 ) which is harmonic in both variables. It is demonstrated that the Huygens bilocality of V 1 can be equivalently characterized by a “single-pole property” concerning the pole structure of the (rational) correlation functions involving the product ϕ 1 (x 1 )ϕ 2 (x 2 ). This property is established for the dimension d=2 of ϕ 1 ,ϕ 2 . As an application we prove that any system of GCI scalar fields of conformal dimension 2 (in four space-time dimensions) can be presented as a (possibly infinite) superposition of products of free massless fields.
MSC:
81T40Two-dimensional field theories, conformal field theories, etc.
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