Lifshitz fermionic theories with z=2 anisotropic scaling

TL;DR

This paper develops fermionic theories with z=2 anisotropic scaling, exploring chiral symmetry, anomalies, and supersymmetric extensions, providing a foundation for Lifshitz fermionic models.

Contribution

It introduces the first fermionic Lagrangians with z=2 anisotropic scaling and analyzes their symmetries, anomalies, and supersymmetric structures.

Findings

Constructed z=2 Lifshitz fermionic Lagrangians.

Analyzed chiral symmetry and anomalies in two dimensions.

Developed supersymmetric extensions of these theories.

Abstract

We construct fermionic Lagrangians with anisotropic scaling z=2, the natural counterpart of the usual z=2 Lifshitz field theories for scalar fields. We analyze the issue of chiral symmetry, construct the Noether axial currents and discuss the chiral anomaly giving explicit results for two-dimensional case. We also exploit the connection between detailed balance and the dynamics of Lifshitz theories to find different z=2 fermionic Lagrangians and construct their supersymmetric extensions.