Bootstrapping the Chiral Anomaly at Large $N_c$

TL;DR

This paper uses bootstrap methods to derive bounds on the chiral anomaly coefficient in gauge theories at large N_c, linking low-energy pion properties to UV theory constraints.

Contribution

It extends bootstrap analysis to pion and gauge boson scattering, providing an analytic bound on the chiral anomaly coefficient based on pion polarizabilities.

Findings

Derived an analytic bound on the chiral anomaly coefficient.

Connected low-energy pion properties to UV theory constraints.

Provided a consistency condition useful for holographic models and lattice simulations.

Abstract

The bootstrap approach (demanding consistency conditions to scattering amplitudes) has shown to be quite powerful to tightly constrain gauge theories at large $N_c$. 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.