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Gravitational Regge bounds
by Kelian Häring, Alexander Zhiboedov
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Kelian Häring |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202312_00011v1 (pdf) |
| Date accepted: | 2024-01-10 |
| Date submitted: | 2023-12-05 15:00 |
| Submitted by: | Häring, Kelian |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We review the basic assumptions and spell out the detailed arguments that lead to the bound on the Regge growth of gravitational scattering amplitudes. The minimal extra ingredient compared to the gapped case - in addition to unitarity, analyticity, subexponentiality, and crossing - is the assumption that scattering at large impact parameters is controlled by known semi-classical physics. We bound the Regge growth of amplitudes both with the fixed transferred momentum and smeared over it. Our basic conclusion is that gravitational scattering amplitudes admit dispersion relations with two subtractions. For a sub-class of smeared amplitudes, black hole formation reduces the number of subtractions to one. Finally, using dispersion relations with two subtractions we derive bounds on the local growth of relativistic scattering amplitudes. Schematically, the local bound states that the amplitude cannot grow faster than $s^2$. The results obtained in the paper are valid for $d> 4$ for which the $2\to2$ scattering amplitude is well-defined.
Author comments upon resubmission
We implemented the requested changes mentioned in the report. We agree that they will help the reader in the lecture of the manuscript.
List of changes
1. We added a sentence in the abstract that the results are derived for d>4 where the gravitational amplitude is well defined.
2. We added the definition of the gravitational amplitude in the first paragraph.
3. We indicated below (1.5) why twice-subtracted dispersion relations are useful.
4. We added an introduction to the "smeared amplitude" in I.b, explaining why it is useful and gave some intuition for it.
5. We emphasise in the caption of Figure.1 and footnote 23 that we only need to compare the powers of s, in comparing the regimes.
6. We elaborated on the "Regularity" assumption in page 4 point 4.
7. We added forward ref to Section III in the point 5, page 5 about Gravitational clustering.
8. We added a sentence in the first paragraph of "III.C. Impact parameter representation" to say that impact parameter provides an intuitive physical picture of large J, large energy scattering.
9. We added below (3.16) that J_alpha are the Bessel function of the first kind.
10. We added references [7-10] at the end of the second paragraph of IV.B
11. We added a sentence below (6.3) to mention that (6.2) and (6.3) are new results.
12. Corrected 1/2 typo in the pre-factor of the tree-level phase shift. Eq. (4.7), (4.17)
Published as SciPost Phys. 16, 034 (2024)
Reports on this Submission
Report
In this paper, the authors revisit the question of the high energy limit of the gravitational interaction. Using non-pertubative unitarity and large impact parameter-space physics, they are able to produce various bounds on the Regge limit of gravitational amplitudes in various dimensions d>=5.
The results are about usual scattering amplitudes and smeared ones, their Regge limit and to a certain extent local growth.
Given the technicality of the subject, and of the results, a great effort as been made to make the results accessible and overall the criteria for publication in Scipost are all met.