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arXiv · 1909.00878

Conformal 3-point functions and the Lorentzian OPE in momentum space

Marc Gillioz
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Abstract

In conformal field theory in Minkowski momentum space, the 3-point correlation functions of local operators are completely fixed by symmetry. Using Ward identities together with the existence of a Lorentzian operator product expansion (OPE), we show that the Wightman function of three scalar operators is a double hypergeometric series of the Appell $F_4$ type. We extend this simple closed-form expression to the case of two scalar operators and one traceless symmetric tensor with arbitrary spin. Time-ordered and partially-time-ordered products are constructed in a similar fashion and their relation with the Wightman function is discussed.

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Marc Gillioz. 2019-09-02. Conformal 3-point functions and the Lorentzian OPE in momentum space. https://doi.org/10.1007/s00220-020-03836-8

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