Non-Abelian twisted kinks in chiral Gross-Neveu model with isospin

The two-dimensional, massless Gross-Neveu model with $N_c$ colors and SU(2) isospin is studied analytically in the large $N_c$ limit. The chiral $\mathrm{SU}(2{)}_L\times \mathrm{SU}(2{)}_R$ symmetry is broken spontaneously in the vacuum. Twisted kinks connecting two arbitrary points on the vacuum manifold $S^3$ are constructed, and their properties are explored. The phase diagram as a function of temperature and baryon and isospin chemical potential is discussed, with special emphasis on inhomogeneous phases. The preferred form of the condensate is a product of the real kink crystal and the chiral spiral. Kink-kink scattering is solved, using the general solution of the multicomponent Bogoliubov–de Gennes equation recently presented by Takahashi.

Figure 1

Example of order parameter $\mathcal{D}=S-i{P}_3$ for the ${\mathrm{isoNJL}}_2$ model at finite density and isospin density. The grid is the surface generated by rotating the real kink crystal order parameter $S(x)$ around the $x$ axis, the fat line is traced out by the order parameter $\mathcal{D}(x)$.

Figure 2

Phase diagram of the ${\mathrm{isoNJL}}_2$ model as a function of $\mu$, ${\mu }_3$, $T$. In the left-hand region under the shaded surface, the radius of the chiral spiral is constant, the pitch increases with ${\mu }_3$. In the right-hand region, the radius is modulated according to $S(x)$, the pitch also increases with ${\mu }_3$. Above the shaded surface, the order parameter vanishes.