In the first part of the talk, we will ask a bedrock question of quantum gravity: Is string theory unique? String amplitudes famously accomplish several extraordinary and interrelated mathematical feats, including an infinite spin tower, tame UV behavior, and dual resonance. I will demonstrate that it is possible to construct infinite new classes of tree-level, dual resonant amplitudes with customizable, nonlinear mass spectra. The construction generalizes naturally to n-point scattering and allows for a worldsheet integral representation. However, these constructions can be strongly constrained using multiparticle factorization, which provides a powerful new set of tools for building consistent amplitudes. In the case of a Regge spectrum, I will investigate whether string amplitudes can be bootstrapped from first principles, finding extra freedom in the dynamics that allows for a new class of dual resonant hypergeometric amplitudes.
In the second part of the talk, I will take a particle physics-driven approach, constraining effective field theories using unitarity and causality. We will construct analytic dispersion relations for the effective field theory of the standard model, bounding the size and sign of higher-dimension operators, with significant implications for CP and flavor violation. These positivity bounds allow us to connect qualitatively different experiments, including predictions for the LHC and precision measurements. I will then apply these tools in a cosmological context, building positivity bounds for the theory of multifield inflation and extracting predictions for non-Gaussianities in the cosmic microwave background.
Taken together, these two complementary initiatives comprise a program unifying phenomenological, formal, and cosmological approaches to high energy physics, bringing together powerful tools bridging fields to map the possibilities of future physics.