  We continue the program [1] of carving out the space of large $N$ confining
gauge theories by modern S-matrix bootstrap methods, with the ultimate goal of
cornering large $N$ QCD. In this paper, we focus on the effective field theory
of massless pions coupled to background electromagnetic fields. We derive the
full set of positivity constraints encoded in the system of 2 $\to$ 2
scattering amplitudes of pions and photons. This system probes a larger set of
intermediate meson states, and is thus sensitive to intricate large $N$
selection rules, especially when supplemented with expectations from Regge
theory. It also has access to the coefficient of the chiral anomaly. We find
novel numerical bounds on several ratios of Wilson coefficients, in units of
the rho mass. By matching the chiral anomaly with the microscopic theory, we
also derive bounds that contain an explicit $N$ dependence.
