SciPost Submission Page
Regge Limit of One-Loop String Amplitudes
by Pinaki Banerjee, Lorenz Eberhardt, Sebastian Mizera
Submission summary
| Authors (as registered SciPost users): | Pinaki Banerjee · Lorenz Eberhardt · Sebastian Mizera |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202507_00011v1 (pdf) |
| Date accepted: | July 30, 2025 |
| Date submitted: | July 2, 2025, 8:33 p.m. |
| Submitted by: | Sebastian Mizera |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
We study the high-energy limit of $2 \to 2$ one-loop string amplitudes at fixed momentum transfer. For the closed string, the high-energy behavior of the amplitudes can be determined from Regge theory just like in field theory, as was first discussed by Amati, Ciafaloni and Veneziano. However, field theory intuition partially breaks down for the open-string amplitude, where amplitudes can exhibit surprising asymptotics in the high-energy limit depending on the topology of the diagram. We call this phenomenon Regge attenuation. We extract Regge limits by a combination of unitarity cuts and saddle-point analysis. We show that the leading contribution of the planar open-string amplitude is sufficiently simple that we can extract it at any loop order. This allows us to resum the genus expansion in a certain limit and demonstrate that the leading Regge trajectory remains linear in that limit.
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
I) At each order in perturbation theory, one studies the scattering amplitude on the real axis of the center-of-mass energy squared $s$. The amplitude has an infinite sequence of poles corresponding to string resonances, whose degrees grow with the loop level. After resumming over all the loop orders, resonances acquire mass shifts and decay widths, which shift the poles to the lower half-plane. Accordingly, the large-$s$ asymptotics of the amplitude at a fixed loop order might be very different from that of the resummed amplitude.
II) A posteriori, anticipating the results of I), one can study the behavior of the scattering amplitude right above the real axis in the complex plane of $s$ even at a fixed order in perturbation theory. The precise direction in the complex plane is once again fixed by the asymptotics of the decay widths. Studying the asymptotic behavior slightly in the upper half-plane can be very different from that along the real axis.
Ultimately, both interpretations are equally valid. The analogy in field theory would be I) resumming 1PI diagrams whose effect is to shift the pole masses and II) adjusting pole masses to be complex at each finite loop order.
In the original submission, we opted for the interpretation I and mentioned II only in passing. According to the referee, II is the only correct interpretation and I is misleading. While we disagree with this point of view, we acknowledge that we have previously not provided a thorough discussion of this issue. In the revised version, we made changes that emphasize both interpretations I and I as outlined below.
We would like to once again thank the referee for their valuable feedback which has contributed to improving the presentation of our results.
List of changes
We made a number of other minor fixes to grammar and presentation throughout the paper.
Published as SciPost Phys. 19, 052 (2025)
Reports on this Submission
Strengths
Weaknesses
Report
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)