QCD worldsheet axion from the bootstrap

The worldsheet axion plays a crucial role in the dynamics of the Yang-Mills confining flux tubes. According to the lattice measurements, its mass is of order the string tension and its coupling is close to a certain critical value. Using the S-matrix Bootstrap, we construct non-perturbative 2 -> 2 branon scattering amplitudes which also feature a weakly coupled axion resonance with these properties. We study the extremal bootstrap amplitudes in detail and show that the axion plays a dominant role in their UV completion in two distinct regimes, in one of which it cannot be considered a parametrically light particle. We conjecture that the actual flux tube amplitudes exhibit a similar behavior.