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Froissart bound for/from CFT Mellin amplitudes
by Parthiv Haldar, Aninda Sinha
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Parthiv Haldar · Aninda Sinha |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202004_00044v5 (pdf) |
| Date accepted: | 2020-06-29 |
| Date submitted: | 2020-06-02 02:00 |
| Submitted by: | Haldar, Parthiv |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We derive bounds analogous to the Froissart bound for the absorptive part of CFTd Mellin amplitudes. Invoking the AdS/CFT correspondence, these amplitudes correspond to scattering in AdSd+1. We can take a flat space limit of the corresponding bound. We find the standard Froissart-Martin bound, including the coefficient in front for d+1=4 being π/μ2, μ being the mass of the lightest exchange. For d>4, the form is different. We show that while for CFTd≤6, the number of subtractions needed to write a dispersion relation for the Mellin amplitude is equal to 2, for CFTd>6 the number of subtractions needed is greater than 2 and goes to infinity as d goes to infinity.
List of changes
Clarifications Added
Various clarifications and comments are added in accordance with the referee reports. These are listed below.
1. Following equation (3.11), it has been mentioned that the flat space limit we are also considering is where R/ℓstrings≫1. This is because in the flat space limit we are considering a massive quantum field theory.
2. In the sentence under (3.2), we have added that the general Mellin amplitude for n−point conformal correlator depends upon n(n−3)/2 independent variables.
3. In section 4.1, various footnotes have been added to add clarifications regarding various assumptions and computational steps. These are delineated in footnotes 5-9.
Typos Fixed
1. In equation (3.26) upper bound of the integral at infinity is fixed.
2. Consistently "flat space" has been used instead of "Flat-space".
3. Notational inconsistency between Γ2(x) and Γ(x)2 has been rectified to stick with Γ2(x).
4. On page 8 penultimate line appendix number has been corrected to G from E.
5. In (B.4) the missing division sign is restored, in (C.9) the 45m2 is corrected to 4m2 and the unmatched parenthesis in (D.7) is taken care of.
6. Spellings corrected at various places and the grammar is improved at places as par the referee recommendation.
Published as SciPost Phys. 8, 095 (2020)
Reports on this Submission
Report #2 by Matthew Dodelson (Referee 2) on 2020-6-15 (Invited Report)
Report
The authors have completed the suggested edits, so I would recommend that the article be published.