The Regge bootstrap, from linear to non-linear trajectories

Abstract: Meromorphic amplitudes are the simplest non-trivial scattering amplitudes. They describe the exchange of infinitely many higher spin resonances in theories like string theory and large N gauge theories. Yet, despite being very simple objects, their numerical bootstrap has proven challenging due to slow convergence of the infinite sums over resonances.
In this talk I will present the content of a recent paper where we managed to implement numerically a linear bootstrap program that allow us to deform scattering amplitudes, starting from the Veneziano amplitude for open strings. The bootstrap heavily relies on Regge theory. In this talk I’ll explain the basics of the bootstrap, mostly how we apply crossing symmetry, the trickiest aspect, and show how it can be used to construct amplitude with phenomenological features of gauge theories.