Harmonic bilocal fields generated by globally conformal invariant scalar fields

Abstract

The twist two contribution in the operator product expansion of phi(1)(x(1)) phi(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 phi(1)(x(1)) phi(2)(x(2)). This property is established for the dimension d = 2 of phi(1), phi(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.