Phase Transitions at Unusual Values of $θ$

We calculate the $θ$ dependence in a cousin of QCD, where the vacuum structure can be analyzed exactly. The theory is N=2 $SU(2)$ gauge theory with NF=0,1,2,3 flavors of fundamentals, explicitly broken to N=1 via an adjoint superpotential, and coupled to anomaly mediated supersymmetry breaking (AMSB). The hierarchy mAMSB μN=1 Λ ensures the validity of our IR analysis. As expected from ordinary QCD, the vacuum energy is a function of $θ$ which undergoes 1st order phase transitions between different vacua where the various dyons condense. For NF=0 we find the expected phase transition at $θ=π$, while for NF=1,2,3 we find phase transitions at fractional values of $π$.