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Zbl 1144.81028
Nikolov, Nikolay M.; Rehren, Karl-Henning; Todorov, Ivan
Harmonic bilocal fields generated by globally conformal invariant scalar fields. (English)
[J] Commun. Math. Phys. 279, No. 1, 225-250 (2008). ISSN 0010-3616; ISSN 1432-0916/e

Summary: 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.

MSC 2000:: *81T40 Two-dimensional field theories, etc.

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Zentralblatt MATH Berlin [Germany]