Lorentz violation in effective field theory and supersymmetry

Violations of Lorentz symmetry and CPT have been entertained as possible phenomenological predictions in theories of quantum gravity. In parallel, various experiments have been searching for the signatures of Lorentz violation. In this talk I describe an effective field theory approach to the problem, and analyze the structure of Lorentz violating operators in expansion over the UV scale (M_Planck). I show that the requirement of supersymmetry imposes strong constraints on possible form of Lorentz violation: it ensures the suppression by at least one power of the UV scale, and forbids any significant modifications of the dispersion relations for particles.