Note on two-dimensional gauged Lifshitz models

TL;DR

This paper fermionizes and bosonizes two-dimensional gauged Lifshitz scalar models to compare their physical modes with Lorentz-invariant theories, revealing similar modes despite different dispersion relations.

Contribution

It introduces a method to analyze gauged Lifshitz models by fermionization and bosonization, highlighting their physical equivalence to Lorentz-invariant models.

Findings

Physical modes match those of Lorentz-invariant theories

Dispersion relations differ between Lifshitz and Lorentz-invariant models

Fermionization and bosonization techniques are effective for analysis

Abstract

We fermionize the two-dimensional free Lifshitz scalar field in order to identify what the gauge covariant couplings are, and then they are bosonized back to get the gauged Lifshitz scalar field theories. We show that they give the same physical modes with those of the corresponding Lorentz invariant gauged scalar theories, although the dispersion relations are different.