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Harmonic bilocal fields generated by globally conformal invariant scalar fields. (English) Zbl 1144.81028
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:
 81T40 Two-dimensional field theories, conformal field theories, etc.
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##### References:
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