On higher-order corrections in a four-fermion Lifshitz model

Abstract

We study a flavour-violating four-fermion interaction in the Lifshitz context, in 3+1 dimensions and with a critical exponent z=3. This model is renormalizable, and features dynamical mass generation, as well as asymptotic freedom. At one-loop, it is only logarithmically divergent, but the superficial degree of divergence of the two-point functions is 3. We calculate the two-loop corrections to the propagators, and show that, at this order, the Lorentz-violating corrections to the IR dispersion relation are quadratic in the cut off. Furthermore, these corrections are too important to represent a physical effect. As a consequence, the predictive power of the model in terms of Lorentz-violating effects in the propagation of particles is limited.

20 pages, 3 figures, comments added

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• Lorentz-Violating Regulator Gauge Fields as the Origin of Dynamical Flavour Oscillations
• Quasi-relativistic fermions and dynamical flavour oscillations
• On the Bhabha scattering for $z=2$ Lifshitz QED
• Effective fermion kinematics from a modified quantum gravity
• One-loop corrections in the z=3 Lifshitz extension of QED
• 1/N Expansion for Horava-Lifshitz like four-fermion models
• Effective matter dispersion relation in quantum covariant Horava-Lifshitz gravity
• Gravitino condensation, supersymmetry breaking and inflation