Scattering and Strebel graphs

TL;DR

This paper explores the connection between scattering equations, Strebel differentials, and graph structures in a special particle scattering setup, revealing a large $n$ limit relationship with matrix models and potential links to the Gross-Mende limit.

Contribution

It establishes a novel link between scattering equations, Strebel differentials, and matrix models, providing insights into the geometric and spectral properties of scattering in high-energy physics.

Findings

Spectral curve relates to Strebel differential on a thrice-punctured sphere.

Solutions localize along graphs influenced by kinematic variables.

Connections to Gross-Mende scattering limit are discussed.

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.