Preprint number: CP3-Origins-2014-17 DNRF90 and DIAS-2014-17
We study the alignment of the vacuum in gauge theories with Nf Dirac fermions transforming according to a complex representation of the gauge group. The alignment of the vacuum is produced by adding a small mass perturbation to the theory. We study in detail the Nf=2,3 and 4 case. For Nf=2 and Nf=3 we reproduce earlier known results including the Dashen phase with spontaneous CP violation. For Nf=4 we find regions with and without spontaneous CP violation similar to the Nf=3 case. Our method is general allowing us to derive a number of results for an arbitrary number of flavors.