Abstract
We define form factors and scattering amplitudes in Conformal Field Theory as the coefficient of the singularity of the Fourier transform of time-ordered correlation functions, as p2 → 0. In particular, we study a form factor F(s, t, u) obtained from a four-point function of identical scalar primary operators. We show that F is crossing symmetric, analytic and it has a partial wave expansion. We illustrate our findings in the 3d Ising model, perturbative fixed points and holographic CFTs.
Highlights
Introduction and summary of resultsScattering amplitudes are among the most important observables in the realm of quantum field theory (QFT)
Crossing symmetry is inherited from the correlator, while the existence of a partial wave decomposition follows from the fact that only a specific partial ordering of the operators contributes to the singularity
We explore the structure of singularities of the Fourier transform of the four-point function of scalar primary operators in a conformal field theory (CFT) in dimension d > 2
Summary
Scattering amplitudes are among the most important observables in the realm of quantum field theory (QFT). This procedure yields the following relation between the form factor and the Mellin amplitude:. While the main focus of this work is on the conformal properties and the OPE decomposition of the form factor and the amplitude, it is interesting to inquire its precise physical meaning. The LSZ procedure discussed here is gauge invariant from the get go, and yields the overlap of special states created by acting with two local operators on the vacuum — see eq (2.51) In this sense, the form factor and the amplitudes are closer in spirit to the event-shape observables described, for instance, in ref. The form factor and the amplitudes are closer in spirit to the event-shape observables described, for instance, in ref. [28]
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