Harmonic bilocal fields generated by globally conformal invariant scalar fields

Nikolay M. Nikolov, Karl-Henning Rehren, Ivan T. Todorov
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;%%" }