On the dynamical origin of the η′ potential and the axion mass

We investigate the dynamics responsible for generating the potential of the eta ', the (would-be) Goldstone boson associated with the anomalous axial U(1) symmetry of QCD. The standard lore posits that pure QCD dynamics generates a confining potential with a branched structure as a function of the theta angle, and that this same potential largely determines the properties of the eta ' once fermions are included. Here we test this picture by examining a supersymmetric extension of QCD with a small amount of supersymmetry breaking generated via anomaly mediation. For pure SU(N) QCD without flavors, we verify that there are N branches generated by gaugino condensation. Once quarks are introduced, the flavor effects qualitatively change the strong dynamics of the pure theory. For F flavors we find |N - F| branches, whose dynamical origin is gaugino condensation in the unbroken subgroup for F < N - 1, and in the dual gauge group for F > N + 1. For the special cases of F = N - 1, N, N + 1 we find no branches and the entire potential is consistent with being a one-instanton effect. The number of branches is a simple consequence of the selection rules of an anomalous U(1)R symmetry. We find that the eta ' mass does not vanish in the large N limit for fixed F/N, since the anomaly is non-vanishing. The same dynamics that is responsible for the eta ' potential is also responsible for the axion potential. We present a simple derivation of the axion mass formula for an arbitrary number of flavors.

Automated summary

In this study, we investigate the dynamics responsible for the generation of the potential of the eta ' and test certain assumptions made in the standard lore of QCD. Our results show that the introduction of quarks qualitatively changes the strong dynamics of the pure theory, and the number of branches in the potential is determined by the selection rules of an anomalous U(1)R symmetry.