CERN Accelerating science

Preprint
Report number	CERN-TH-2025-202 ; arXiv:2510.19909
Title	From Partons to Strings: Scattering on the Coulomb Branch of $\mathcal{N}=4$ SYM
Author(s)	Alday, Luis F. (Oxford U., Inst. Math.) ; Armanini, Elisabetta (CERN ; EPFL, Lausanne, FSL) ; Häring, Kelian (Delta ITP, Amsterdam) ; Zhiboedov, Alexander (CERN)
Document contact	Contact: arXiv
Imprint	2025-10-22
Number of pages	109
Note	109 pages, 37 figures, 1 ancillary Mathematica notebook
Subject category	hep-th ; Particle Physics - Theory
Abstract	We study scattering on the Coulomb branch of planar ${\mathcal{N}}=4$ SYM at finite 't Hooft coupling. This setup defines 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. We focus on the four-point amplitude, which exhibits a remarkably rich structure: nonlinear Regge trajectories, dual conformal invariance, an intricate spectrum of bound states with an accumulation point, and a two-particle cut. Dual conformal invariance relates the spectrum of Regge trajectories to the energy spectrum of the Maldacena-Wilson cusp Hamiltonian. This connection allows us to use integrability to compute the leading and subleading Regge trajectories at finite coupling, which we then input in the bootstrap analysis. At strong coupling, we use the worldsheet bootstrap to construct the first $AdS$-curvature correction to the Veneziano amplitude. We apply dispersion relations and S-matrix bootstrap techniques to derive bounds on Wilson coefficients, couplings to bound states, and the overall shape of the amplitude. We find that the $\mathcal{N}=4$ amplitude saturates the bootstrap bounds at weak coupling and nearly saturates them at strong coupling. At intermediate coupling, the amplitude traces a nontrivial path through the allowed space of observables. To characterize this path, we combine the weak- and strong-coupling information about the amplitude to construct a finite-coupling model for Wilson coefficients using a Padé approximation. The resulting model satisfies bootstrap constraints and yields sharp predictions for the finite-coupling behavior of the amplitude. We provide evidence that complete monotonicity of the scattering amplitude, previously observed perturbatively, persists at finite coupling.
Other source	Inspire
Copyright/License	preprint: (License: CC BY 4.0)