I will discuss scattering on the Coulomb branch of planar N=4 SYM at finite ’t Hooft coupling. This describes a family of classical open-string S-matrices that smoothly interpolates between perturbative parton scattering at weak coupling and flat-space string scattering at strong coupling. I will focus on the four-point amplitude and discuss its remarkably rich structure: nonlinear Regge trajectories, dual conformal invariance, an intricate spectrum of bound states with an accumulation point, and a two-particle cut. Using dispersion relations and S-matrix bootstrap techniques, these properties can be incorporated to constrain the amplitude at finite ’t Hooft coupling, and I will discuss bounds on Wilson coefficients, couplings to bound states, and the overall shape of the amplitude.

This is based on https://arxiv.org/abs/2510.19909.