Landau-Peierls instability in a Fulde-Ferrell type inhomogeneous chiral condensed phase

We investigate the stability of an inhomogeneous chiral condensed phase against low energy fluctuations about a spatially modulated order parameter. This phase corresponds to the so-called dual chiral density wave in the context of quark matter, where the chiral condensate is spatially modulated with a finite wavevector in a single direction. From the symmetry viewpoint, the phase realizes a locking of flavor and translational symmetries. Starting with a Landau-Ginzburg-Wilson effective Lagrangian, we find that the associated Nambu-Goldstone modes, whose dispersion relations are spatially anisotropic and soft in the direction normal to the wavevector of the modulation, wash out the long-range order at finite temperatures, but support algebraically decaying long-range correlations. This implies that the phase can exhibit a quasi-one-dimensional order as in liquid crystals.