We calculate the θ dependence in a cousin of QCD, where the vacuum structure can be analyzed exactly. The theory is \( \mathcal{N} \) = 2 SU(2) gauge theory with NF = 0, 1, 2, 3 flavors of fundamentals, explicitly broken to \( \mathcal{N} \) = 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.
