At large number of colours, a confining gauge theory becomes a theory
of weakly interacting hadrons, with mesons forming a closed subsector.
In this context, constraining the masses and couplings of mesons is a
well-defined and tractable bootstrap problem. In my talk, I will
review the EFT bootstrap and show how it applies to meson scattering.
Specifically, I will explain how a few simple but carefully chosen
assumptions lead us to an extremal amplitude featuring a Regge
trajectory with mesons at all spins, and numerical data remarkably
close to real-world QCD.