Schwinger-Dyson approach for a Lifshitz-type Yukawa model

TL;DR

This paper uses the Schwinger-Dyson approach to analyze a Lifshitz-type Yukawa model, showing dynamical generation of fermion kinetic and mass terms, indicating Lorentz symmetry restoration in the IR.

Contribution

It introduces a non-perturbative analysis of a Lifshitz Yukawa model, revealing dynamical fermion mass and kinetic term generation and discussing Lorentz symmetry restoration.

Findings

Dynamical generation of fermion mass and kinetic terms

Restoration of Lorentz symmetry in the IR regime

Limitations discussed for multi-fermion theories

Abstract

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. The limitations of the model and our approach are discussed.