Effective description of the LOFF phase of QCD

We present an effective field theory for the crystalline color super-conductivity phase of QCD. It is kown that at high density and at low temperature QCD exhibits a transition to a color superconduct-ing phase characterized by energy gaps in the fermion spectra. Under specific circumstances the gap parameter has a crystalline pattern, breaking translational and rotational invariance. The corresponding phase is the crystalline color superconductive phase (or LOFF phase). We compute the parameters of the low energy effective lagrangian describing the motion of the free phonon in the high density medium and derive the phonon dispersion law.