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The phase structure of dense quark matter in the two color case has beeninvestigated with nonzero baryon $\mu_B$, isospin $\mu_I$ and chiral isospin$\mu_{I5}$ chemical potentials. %in the framework of Nambu--Jona-Lasinio modelwith quark-antiquark and quark-quark interaction channels. It has been shown inthe mean-field approximation that there exist three dualities, one of thembetween phases with spontaneous chiral symmetry breaking and condensation ofcharged pions, found in the three color case. The other two dual symmetriesbetween the phase with condensation of charged pions and the phase with diquarkcondensation and between chiral symmetry breaking and diquark condensationphenomena. It has been demonstrated that due to the duality properties thephase diagram is extremely symmetric and the whole phase diagram in two colorcase can be obtained just by dualities from the phase structure of three colorcase. This shows that the dualities are rather usefull tool. It is shown thatchiral imbalance generates charged pion condensation phenomenon in conditionsof matter in neutron stars, i. e. electrically neutral and $\beta$-equilibrateddense quark matter. And that diquark condensation does not prohibit thegeneration of the charged PC phase by chiral imbalance at least in the twocolor case.

The phase structure of two color QCD and charged pion condensation phenomenon