The bootstrap approach (demanding consistency conditions to scattering
amplitudes) has shown to be quite powerful to tightly constrain gauge theories
at large Ncβ. We extend previous analysis to scattering amplitudes involving
pions and external gauge bosons. These amplitudes allow us to access the chiral
anomaly and connect low-energy physical quantities to UV properties of the
theory. In particular, we are able to obtain an analytic bound on the chiral
anomaly coefficient as a function of the pion dipole polarizabilities. This
bound can be useful for holographic models whose dual UV completions are not
known, and provide a consistency condition to lattice simulations.Comment: 20 pages, 1 figure. v2: bound on the anomaly generalised and typos
correcte