Effective Potential For Lifshitz-Type Z=3 Gauge Theories

We consider the one-loop effective potential at zero temperature in Lifshitz-type field theories with anisotropic space-time scaling, with critical exponent z = 3, including scalar, fermion and gauge fields. The fermion determinant generates a symmetry breaking term at one loop in the effective potential and a local minimum appears, for nonzero scalar field, for every value of the Yukawa coupling. Depending on the relative strength of the coupling constants for the scalar and the gauge field, we find a second symmetry breaking local minimum in the effective potential for a bigger value of the scalar field.