Low-Energy Lorentz Invariance in Lifshitz Nonlinear Sigma Models

TL;DR

This paper investigates the quantum properties of Lifshitz nonlinear sigma models with z=2 in 2+1 dimensions, focusing on renormalization, Lorentz invariance emergence at low energies, and supersymmetric extensions.

Contribution

It provides a comparative analysis of Lorentz invariance restoration in large-N versus perturbative frameworks for Lifshitz sigma models.

Findings

Lorentz invariance can emerge at low energies in the large-N approach.

Restoration of Lorentz symmetry is more delicate in perturbative expansion.

Supersymmetric extensions are considered in the nonrelativistic context.

Abstract

This work is dedicated to the study of both large-$N$ and perturbative quantum behaviors of Lifshitz nonlinear sigma models with dynamical critical exponent $z=2$ in 2+1 dimensions. We discuss renormalization and renormalization group aspects with emphasis on the possibility of emergence of Lorentz invariance at low energies. Contrarily to the perturbative expansion, where in general the Lorentz symmetry restoration is delicate and may depend on stringent fine-tuning, our results provide a more favorable scenario in the large-$N$ framework. We also consider supersymmetric extension in this nonrelativistic situation.