A Scattering Amplitude in Conformal Field Theory

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 $p^2\to 0$. 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.

arXiv comment70 pages, 15 figures

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Cited by in corpus (16)

• Linking the Singularities of Cosmological Correlators
• Dispersive CFT Sum Rules
• Conformal correlators as simplex integrals in momentum space
• Double copy structure of parity-violating CFT correlators
• The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization
• Higher spin 3-point functions in 3d CFT using spinor-helicity variables
• Distributions in CFT II. Minkowski Space
• Momentum space parity-odd CFT 3-point functions
• Constraining momentum space correlators using slightly broken higher spin symmetry
• Generalizing event shapes: In search of lost collider time
• A Scattering Amplitude for Massive Particles in AdS
• Conformal partial waves in momentum space
• AdS correction to the Faddeev-Kulish state: Migrating from the Flat Peninsula
• General Freeze-in and Freeze-out
• ANEC in $\lambda {\varphi }^4$ theory
• Anomalous Ward identities for on-shell amplitudes at the conformal fixed point