Gluonic phases and phase diagram in neutral two flavor dense QCD

A numerical analysis of several phases in the cold neutral two flavor dense quark matter is realized. In the analysis, besides the normal, single plane wave LOFF, and color superconducting 2SC/g2SC phases, we also include two gluonic phases (the gluonic cylindrical phase II and the gluonic color-spin locked one). It is shown that these two gluonic phases are dynamically realized and, on the basis of this analysis, the phase diagram with respect to the coupling strength in this medium is suggested. In particular, it is shown that the gluonic phases are energetically favorable in a wide region of the parameter space and they can resolve the problem of the 2SC/g2SC chromomagnetic instability in the whole region where it exists. On the other hand, there also exists a window where the LOFF phase is stable. The 2SC state and the normal one are realized in the strong and weak coupling regimes, respectively, as was expected.