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The High Density Effective Theory formalism is used to calculate the lowenergy properties of the phonons and gluons in theLarkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase of two-flavor QCD. The effectivephonon Lagrangian for the cubic crystal structure, which is favored accordingto a recent study, depends, at the second order in the derivatives, on threeparameters which we calculate in this paper. We also compute for soft momentathe effective lagrangian for the gluons of the unbroken SU(2)_c group, both fora single plane wave structure and for the cube. In both cases the Meissnergluon mass vanishes as in the case of complete isotropy; on the other handthere is a partial Debye screening due to the existence of blocking regions onthe Fermi spheres. For the single plane wave structure the gluon dielectrictensor is non isotropic, while it is isotropic for the cubic crystal, in spiteof the intrinsic anisotropy of the structure.Comment: 38 pages, 4 figure

Phonons and gluons in the crystalline color superconducting phase of QCD