Appearance of novel modes of $\bar{D}$ mesons in the Dual Chiral Density Wave

We calculate dispersion relations for $\bar{D}(0^{-})$, ${\bar{D}}^{\ast }(1^{-})$, ${\bar{D}}_0^{\ast }(0^{+})$ and ${\bar{D}}_1(1^{+})$ mesons in the Dual Chiral Density Wave (DCDW) where the chiral symmetry is spontaneously broken by inhomogeneous chiral condensate. Employing the Bloch’s theorem, we show that all the modes have opposite group velocity to the momentum in the low-momentum region and the energy is minimized at non-zero momentum. Furthermore, the magnitude of momentum which realizes the minimum energy is equal to the wave number of the density wave.