Bootstrapping meson scattering amplitudes at large N

In the bootstrap approach in theoretical physics we derive bounds on physical observables from mathematical self-consistency and basic physical principles such as unitarity. In this talk, I will apply modern numerical bootstrap techniques to an old problem, namely that of predicting the masses and couplings of strongly interacting mesons and baryons. Working at large number of colours $N$, the scattering of mesons forms a closed system where the scattering amplitudes are meromorphic functions with poles at meson masses. I will review previous work on pion scattering in this context, and then present results from ongoing work on rho meson scattering. In the latter case, we observe an interesting feature at our bound, saturated by a $J^{PC}=2^{++}$ state with a mass approximately equal to that of the lightest physical spin-2 meson ($f_2$). This work is part of a longer programme towards a bootstrap determination of the spectrum of large-N QCD.