In this talk, I will describe an analytic procedure whereby scattering amplitudes are bootstrapped directly from an input mass spectrum and a handful of physical constraints: crossing symmetry, boundedness at high energies, and finiteness of exchanged spins. For an integer spectrum, this procedure gives a first principles derivation of a new infinite parameter generalization of the Veneziano amplitude that is unitary while exhibiting dual resonance and consistent high-energy behavior. Lifting to a q-deformed integer spectrum, I will derive the Coon amplitude and its analogous generalizations. Finally, I will apply this logic to derive an infinite class of deformed Virasoro-Shapiro amplitudes.

https://princeton.zoom.us/j/97248927011?pwd=SWFiNWFwZWE5SUR4OUxvV0ZacVd…