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arXiv · 0704.1960

Harmonic bilocal fields generated by globally conformal invariant scalar fields

Nikolay M. Nikolov·Karl-Henning Rehren·Ivan Todorov
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Abstract

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.

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Nikolay M. Nikolov, Karl-Henning Rehren, Ivan Todorov. 2008-01-16. Harmonic bilocal fields generated by globally conformal invariant scalar fields. https://doi.org/10.1007/s00220-007-0394-0

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