Abstract
The twist two contribution in the operator product expansion of \(\phi_{1} ({\rm x}_{1})\phi_{2}({\rm x}_{2})\) for a pair of globally conformal invariant, scalar fields of equal scaling dimension d in four space–time dimensions is a field V 1 (x1, x2) 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 \(\phi_{1}({\rm x}_{1})\phi_{2}({\rm x}_{2})\). 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.
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Communicated by Y. Kawahigashi
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Nikolov, N.M., Rehren, KH. & Todorov, I. Harmonic Bilocal Fields Generated by Globally Conformal Invariant Scalar Fields. Commun. Math. Phys. 279, 225–250 (2008). https://doi.org/10.1007/s00220-007-0394-0
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DOI: https://doi.org/10.1007/s00220-007-0394-0