# Harmonic bilocal fields generated by globally conformal invariant scalar fields

April 16, 2007

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 GCI scalar field of conformal dimension 2 (in four space-time dimensions) can be written as a (possibly infinite) superposition of products of free massless fields.

open access link
Commun. Math. Phys. 279 (2008) 225-250

@article{Nikolov:2007nt,
author = "Nikolov, Nikolay M. and Rehren, Karl-Henning and Todorov,
Ivan",
title = "{Harmonic bilocal fields generated by globally conformal
invariant scalar fields}",
journal = "Commun. Math. Phys.",
volume = "279",
year = "2008",
pages = "225-250",
doi = "10.1007/s00220-007-0394-0",
eprint = "0704.1960",
archivePrefix = "arXiv",
primaryClass = "hep-th",
SLACcitation = "%%CITATION = ARXIV:0704.1960;%%"
}

Keywords:

*none*