In this paper the phase structure of dense baryon matter composed of u and d quarks with two colors has been investigated in the presence of baryon μ B , isospin μ I and chiral isospin μ I 5 chemical potentials in the framework of Nambu-Jona-Lasinio model with quark-antiquark and quark-quark interaction channels. In the chiral limit, it has been shown in the mean-field approximation that the duality between phases with spontaneous chiral symmetry breaking and condensation of charged pions, found in the three color case, remains valid in the two color case. In addition, it has been shown that there are two more dualities in the phase diagram in two color case, namely (as in the case with μ I 5 = 0), at μ I 5 ≠ 0 the general ( μ, μ I , μ I 5 )-phase portrait of the model has dual symmetry between the phase with condensation of charged pions and the phase with diquark condensation. This duality stays exact even in the physical point, m 0 ≠ 0. And at m 0 = 0 the ( μ, μ I , μ I 5 )- phase portrait becomes even more symmetrical, since dual symmetry between phases with spontaneous chiral symmetry breaking and diquark condensation appears. It is shown that due to the dualities the phase diagram is extremely symmetric and has interlacing structure. One can show that the phase portrait of two-color NJL model can be obtained just by duality properties from the results of investigations of three-color NJL model (it was noticed only after the numerical calculations have been performed). Three-color case shares only one duality of the two color one, and one can only see a facet of this enormously symmetric picture in the case of three colors. Using dualities only, it is possible to show that there are no mixed phases (phases with two non-zero condensates). This prediction of dualities is of great use, because for sure it can be shown by the direct calculations but it would be enormously more complicated and time-consuming numerically.

中文翻译：

---

由双色夸克形成的手性和同位旋不对称致密夸克物质的双重性质

本文研究了重子 μ B 、同位旋 μ I 和手性同位旋 μ I 5 化学势在 Nambu-Jona-Lasinio 框架下由两种颜色的 u 和 d 夸克组成的致密重子物质的相结构。夸克-反夸克和夸克-夸克相互作用通道的模型。在手征极限中，平均场近似表明，在三色情况下发现的自发手征对称性破坏和带电介子凝聚相之间的二元性在两种颜色情况下仍然有效。此外，已经表明，在两种颜色的情况下，相图中还有两个对偶性，即（如在 μ I 5 = 0 的情况下），在 μ I 5 ≠ 0 时，一般 ( μ, μ I , μ I 5 )-模型的相图在带电介子凝聚相和狄夸克凝聚相之间具有双重对称性。即使在物理点，这种对偶性也保持精确，m 0 ≠ 0。并且在 m 0 = 0 时，( μ, μ I , μ I 5 )-相图变得更加对称，因为相之间的双重对称性自发手征对称性破坏并出现狄夸克凝聚。结果表明，由于二元性，相图非常对称并且具有交错结构。从三色NJL模型的研究结果可以看出，仅通过对偶性质就可以得到双色NJL模型的相图（这是在进行数值计算后才注意到的）。三色表壳只共享二色一的一种二元性，在三种颜色的情况下，人们只能看到这张极其对称的图片的一个方面。仅使用对偶性，可以证明不存在混合相（具有两个非零冷凝物的相）。这种对偶性的预测很有用，因为它肯定可以通过直接计算来显示，但在数值上会更加复杂和耗时。