Bootstrapping mesons at large $N$: Regge trajectory from spin-two maximization

We continue the investigation of large $N$ QCD from a modern bootstrap perspective, focusing on the mesons. We make the natural spectral assumption that the $2\to 2$ pion amplitude must contain, above the spin-one rho meson, a massive resonance of spin two. By maximizing its coupling we find a very interesting extremal solution of the dual bootstrap problem, which appears to contain at least a full Regge trajectory. Its low-lying states are in uncanny quantitative agreement with the meson masses in the real world.