Repercussions of the Peccei–Quinn axion on QCD

The axion, originally postulated by Peccei and Quinn to solve the strong CP problem, has become of great interest in particle and astroparticle phenomenology. Yet it has a problem. It is widely assumed that the axion leaves the nonperturbative features of QCD unscathed. This is, however, not the case. On the contrary, the axion extension is found to be in conflict with seminal results on the low-energy properties of QCD. The key is that the anomalous coupling of the axion to the gauge bosons can be integrated out, leaving behind a path integral over topologically trivial gauge potentials.