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Flat-space Partial Waves From Conformal OPE Densities
by Balt C. van Rees, Xiang Zhao
Submission summary
| Authors (as registered SciPost users): | Xiang Zhao |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2312.02273v2 (pdf) |
| Date submitted: | 2024-03-08 09:22 |
| Submitted by: | Zhao, Xiang |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We consider the behavior of the OPE density $c(\Delta,\ell)$ 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 $f_\ell(s)$ 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.
Current status:
In refereeing