The Regge bootstrap, from linear to non-linear trajectories

We present a numerical linear programming bootstrap to construct dual model scattering amplitudes. Dual models describe tree-level exchanges of higher spin resonances in theories like string theory and large $N$ gauge theories. Despite being very simple objects, their numerical bootstrap has proven challenging due to slow convergence of the infinite sums over resonances. Our bootstrap succeeds thanks to an efficient parametrization of the amplitude in terms of Mandelstam-Regge poles and the use of combined regions that make crossing symmetry constraining. Along the way, we discover and conjecture a property of "super-unitarity" of the Veneziano amplitude, which we use to keep a linear problem. As results, we present first the study of a class of string-like amplitudes with linear trajectories, for which we observe that the Veneziano amplitude lies at a preferred location, at the bottom of a pit, which minimizes crossing. Then, we introduce a toy-model deformation to non-linear trajectories, mimicking some features of QCD, for which our algorithm also detects a clear pit. This gives compelling evidence that our bootstrap is able to produce amplitudes that can exhibit non-trivial phenomenological features.