Harmonic bilocal fields generated by globally conformal invariant scalar fields
Abstract
The twist two contribution in the operator product expansion of phi1(x1) phi2(x2) for a pair of globally conformal invariant, scalar fields of equal scaling dimension d in four space-time dimensions is a field V1(x1,x2) which is harmonic in both variables. It is demonstrated that the Huygens bilocality of V1 can be equivalently characterized by a "single-pole property" concerning the pole structure of the (rational) correlation functions involving the product phi1(x1) phi2(x2). This property is established for the dimension d=2 of phi1, phi2. 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.