"A Bootstrap bridge between Gravity and QCD"
The numerical S-matrix Bootstrap establishes non-perturbative universal bounds on physical observables extracted from scattering amplitudes in any dimension. In this talk, I will discuss three results: rigorous model-independent bounds on Higgs couplings, the Bootstrap of the physical QCD spectrum from glueballs and pion scattering, and no-go theorems for supersymmetric Quantum Gravity. These results are possible by going beyond the positivity of scattering amplitudes, including the non-linear unitarity inequalities. Taming the non-linear unitarity constraints requires both an analytic and technological effort. During the discussion, I will describe the Bootstrap methodology and the numerical challenges we face when tackling these problems. I will conclude with a list of possible future directions that are interesting for the development of the field.
