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.
Cite
@article{arxiv.0704.1960,
title = {Harmonic bilocal fields generated by globally conformal invariant scalar fields},
author = {Nikolay M. Nikolov and Karl-Henning Rehren and Ivan Todorov},
journal= {arXiv preprint arXiv:0704.1960},
year = {2008}
}
Comments
29 pages. v2: corrected an argument, v4: final version as to be published in CMP