A bstract We calculate the θ dependence in a cousin of QCD, where the vacuum structure can be analyzed exactly. The theory is N N = 2 SU (2) gauge theory with N F = 0, 1, 2, 3 flavors of fundamentals, explicitly broken to N 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.
Csáki et al. (Mon,) studied this question.