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 N_F = 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 m_AMSB ≪ μ_N=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 N_F = 0 we find the expected phase transition at θ = π, while for N_F = 1, 2, 3 we find phase transitions at fractional values of π.