Flat-space Partial Waves From Conformal OPE Densities

2023/12/04 by Balt C. van Rees, Xiang Zhao, van Rees, Balt C. +1 · 3 citations
Physics and Astronomy · Earth and Planetary Sciences · #Black Holes and Theoretical Physics #Quantum Chromodynamics and Particle Interactions #Seismic Imaging and Inversion Techniques

paper · pdf · doi:10.48550/arxiv.2312.02273

Abstract

We consider the behavior of the OPE density c(Δ,ℓ) for conformal four-point functions in the flat-space limit where all scaling dimensions become large. We find evidence that the density reduces to the partial waves f_ℓ(s) of the corresponding scattering amplitude. The Euclidean inversion formula then reduces to the partial wave projection and the Lorentzian inversion formula to the Froissart-Gribov formula. The flat-space limit of the OPE density can however also diverge, and we delineate the domain in the complex s plane where this happens. Finally we argue that the conformal dispersion relation reduces to an ordinary single-variable dispersion relation for scattering amplitudes.

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