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.
Highlights
Conformal field theory can be formulated algebraically in terms of a set of primary operators and of rules that define the operator product expansion (OPE)
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 F4 type
Summary
Conformal field theory can be formulated algebraically in terms of a set of primary operators and of rules that define the operator product expansion (OPE). Even in the simplest case of 3 scalar operators, the only expression available in the literature so far is in the form of a quite complicated integral over Bessel functions [24] In spite of these difficulties, there exist strong motivations to study conformal field theory in Minkowski momentum space. With this strategy, we do not perform directly the Fourier transform of the position-space correlation function, we use it to verify numerically and in some limits analytically the validity of our derivation. We present the direct Fourier transform of the positionspace correlation function used to verify our results numerically
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