  We revisit from a modern bootstrap perspective the longstanding problem of
solving QCD in the large $N$ limit. We derive universal bounds on the effective
field theory of massless pions by imposing the full set of positivity
constraints that follow from $2 \to 2$ scattering. Some features of our
exclusion plots have intriguing connections with hadronic phenomenology. The
exclusion boundary exhibits a sharp kink, raising the tantalizing scenario that
large $N$ QCD may sit at this kink. We critically examine this possibility,
developing in the process a partial analytic understanding of the geometry of
the bounds.

High Energy Physics - Theory;High Energy Physics - Phenomenology