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Lorentzian contours for tree-level string amplitudes
by Lorenz Eberhardt, Sebastian Mizera
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Lorenz Eberhardt · Sebastian Mizera |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202408_00015v1 (pdf) |
| Date accepted: | 2024-08-26 |
| Date submitted: | 2024-08-14 15:12 |
| Submitted by: | Mizera, Sebastian |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We engineer compact contours on the moduli spaces of genus-zero Riemann surfaces that achieve analytic continuation from Euclidean to Lorentzian worldsheets. These generalized Pochhammer contours are based on the combinatorics of associahedra and make the analytic properties of tree-level amplitudes entirely manifest for any number and type of external strings. We use them in practice to perform first numerical computations of open and closed string amplitudes directly in the physical kinematics for $n=4,5,6,7,8,9$. We provide a code that allows anyone to do such computations.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
List of changes
In response to Referee 1:
1) Following the referee's advice, we included pointers to the high-energy fixed-angle limit discussion already in the Introduction. We also changed the title of Sec. 3.5 to highlight it contains a discussion of this topic. We further expanded Sec. 4.4 with comments on the high-energy limit in the closed-string case.
2) Even though the presence of Stokes phenomena in string scattering is known to experts, we are not aware of a reference where it has been thoroughly investigated. Instead, as a pointer to the literature, we included a reference to our recent paper 2403.07064 that discusses these issues in the Regge limit at genus one.
3) We've corrected SL(2,C) to SL(2,R). Thank you for spotting this typo.
4) We decided to not spell out examples for n > 4, because in even in the matrix form they would not fit within the margins. We commented that they can be efficiently computed using the Mathematica code attached to Ref. [31].
5) We've included the additional reference.
6) Thank you, these typos are now fixed.
In response to Referee 2:
1) We agree that the previous wording on Sec. 2.2 might've appeared confusing. We changed the first paragraph to emphasize that the closed-string moduli space is only introduced as a complexification of the open-string one. It so happens that the same space is later used for close-string scattering.
2) Thank you, this typos is now fixed.
Published as SciPost Phys. 17, 078 (2024)