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

2019

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

Gillioz, Marc

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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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