Effective field theory for the crystalline colour superconductive phase of QCD

Abstract We present an effective field theory for high density, low temperature QCD in the crystalline colour superconductive phase ( LOFF phase). This interesting phase of QCD is characterized by a gap parameter with a crystalline pattern, breaking translational and rotational invariance, and could have astrophysical applications. In the effective theory the fermions have a Majorana mass, which, besides colour, breaks translation and rotation symmetries. Fermions couple to the phonon arising from the breaking of rotation and translation invariance. Integrating out the fermions leads eventually to an effective Lagrangian in terms of the phonon field only, which satisfies an anisotropic dispersion relation.