θ-parameter in 2 color QCD at finite baryon and isospin density

We use 2-color QCD as a model to study the effects of simultaneous presence of the so-called θ parameter, chemical potentials for baryon number, μB and for isospin charge, μI. We pay special attention to θ, μB, μI dependence of different vacuum condensates, including chiral and diquark condensates, as well as the gluon condensate, 〈bg232π2GμνaGμνa〉, and the topological susceptibility. We find that two phase transitions of the second order will occur when θ relaxes from θ=2π to θ=0, if μ is of order of the pion mass, mπ. We demonstrate that the transition to the superfluid phase at θ=π occurs at a much lower chemical potential than at θ=0. We also show that the strong θ dependence present near θ=π in vacuum (Dashen's phenomenon), becomes smoothed out in the superfluid phase. Finally, we comment on the relevance of this study for the real world with Nc=3.