Schwinger-Dyson approach for a Lifshitz-type Yukawa model

Understand

We consider a 3+1 dimensional field theory at a Lifshitz point for a dynamical critical exponent z=3, with a scalar and a fermion field coupled via a Yukawa interaction.

• Using the non-perturbative Schwinger-Dyson approach we calculate quantum corrections to the effective action.
• We demonstrate that a first order derivative kinetic term as well as a mass term for the fermion arise dynamically.
• This signals the restoration of Lorentz symmetry in the IR regime of the single fermion model, although for theories with more than one fermionic species such a conclusion will require fine-tuning of couplings.