## 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. in quantum mechanics
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### References:

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