Schwinger-Dyson approach for a Lifshitz-type Yukawa model

Details Schwinger-Dyson approach for a Lifshitz-type Yukawa model Schwinger-Dyson approach for a Lifshitz-type Yukawa model

2009-09-21

arxiv.org/abs/0909.3719v2

Phys.Rev.D81:045002,2010

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, 2 figures

Scientific paper

10.1103/PhysRevD.81.045002

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.

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