Bootstrapping Stringy Amplitudes
String amplitudes famously accomplish several extraordinary and interrelated mathematical feats, including an infinite spin tower, tame UV behavior, and dual resonance: the ability of the amplitude to be represented as a sum over a single scattering channel. But how unique are these properties to string amplitudes? In this talk, I will demonstrate that it is possible to construct infinite new classes of tree-level, dual resonant amplitudes with customizable, nonlinear mass spectra. The structures generalize naturally to n-point scattering and allow for worldsheet integral representations. Using multiparticle factorization, I will develop a formalism for imposing unitarity of higher-point scattering, finding stringent constraints on deformations of string amplitudes. In the case of a Regge spectrum, I will investigate whether the structure of the four-point Veneziano amplitude can be bootstrapped from first principles. We will find that there is extra apparent freedom in the dynamics, allowing for a new class of dual resonant hypergeometric amplitudes with a linear spectrum.