Renormalization group approach in a Lifshitz-like Gross-Neveu-Thirring model

In this work, we use the renormalization group method in the study of the behavior of a quartic fermionic self-interaction in a Gross-Neveu-Thirring model in 2+1 dimensions, in the context of Hořava-Lifshitz theory. We show that if we include high derivatives in the spatial part of the free Lagrangian density for a critical exponent z=2 the model becomes renormalizable by power counting, thus improving the ultraviolet (UV) behavior of theory. We determine the renormalization group (RG) functions at one-loop order and we obtain the fixed points of effective beta function (β). We find that it is asymptotically free for the case β<0.