The η' is the (would-be) Goldstone boson associated with the anomalous U(1) axial symmetry of QCD. Very little is known about its potential away from the limit of a large number of colors. In QCD, where the number of colors and quark flavors is comparable, we do not even know if it is a single-valued function or if, instead, it has multiple branches. To shed some light on the η' in QCD, I will discuss an exact calculation of its potential in supersymmetric QCD with small supersymmetry breaking from anomaly mediation and an arbitrary number of flavors F and colors N. I will then draw some lessons valid for ordinary QCD and discuss the implications of our results for the axion potential.
