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Scattering and Strebel graphs
by Pronobesh Maity
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Submission summary
| Authors (as registered SciPost users): | Pronobesh Maity |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2108.09458v2 (pdf) |
| Date accepted: | 2022-07-05 |
| Date submitted: | 2022-06-08 20:14 |
| Submitted by: | Maity, Pronobesh |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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Abstract
We consider a special scattering experiment with n particles in $\mathbb{R}^{n-3,1}$. The scattering equations in this set-up become the saddle-point equations of a Penner-like matrix model, where in the large $n$ limit, the spectral curve is directly related to the unique Strebel differential on a Riemann sphere with three punctures. The solutions to the scattering equations localize along different kinds of graphs, tuned by a kinematic variable. We conclude with a few comments on a connection between these graphs and scattering in the Gross-Mende limit.
List of changes
The following changes have been made:
1. Reference [13] https://inspirehep.net/literature/1835427 has been added.
2. $\mathbb{R}^{d-1,1}$ has been replaced by $\mathbb{R}^{1,d-1}$ throughout the text.
3. In eq. (2.6), $j(\neq 1)=1$ has been replaced by $j(\neq i)=1$.
4. In eq. (3.13) and (3.18), integration contour C has been replaced by $\mathcal{C}.
5. In eq. (6.1) and (6.2), $\mathcal{O}(1/s)$ has been removed.
6. In eq (B.3), $i \leq j$ is replaced by $i<j$.
7. In the 2nd line of eq. (3.3), the Vandermonde determinant $\Delta^2(\{\sigma_a\})$ has been removed.
8. Above eq. (2.7) we mentioned that three redundant scattering eq.s are removed and below the eq. we specified the choices of $\sigma_{A,B,C}$ explicitly.
9. Below eq. (2.3), we mentioned that the on-shell condition is satisfied.
10. In eq. (2.9), we added a -ve sign on the L.H.S.
11. Added a line "But a good analytical method is still missing" in the 2nd stanza of page 1.
12. Corrected the typo from "chqnge" to "change" below eq. (B.3).
Published as SciPost Phys. 13, 010 (2022)