On Higher Spatial Derivative Field Theories

TL;DR

This paper investigates field theories with anisotropic scaling using renormalization group techniques, analyzing Lorentz symmetry breaking effects with and without higher spatial derivatives in scalar and fermionic models.

Contribution

It provides a comprehensive analysis of Lorentz symmetry breaking in higher spatial derivative field theories employing renormalization group methods.

Findings

Lorentz breaking can be soft or complex depending on higher derivatives.

Higher spatial derivatives influence the renormalization group flow.

Scalar and fermionic models exhibit distinct symmetry breaking behaviors.

Abstract

In this work, we employ renormalization group methods to study the general behavior of field theories possessing anisotropic scaling in the spacetime variables. The Lorentz breaking symmetry that accompanies these models are either soft, if no higher spatial derivative is present, or it may have a more complex structure if higher spatial derivatives are also included. Both situations are discussed in models with only scalar fields and also in models with fermions as a Yukawa like model.