RG Flows and Symmetry Enhancement in Five-Dimensional Lifshitz Gauge Theories

TL;DR

This paper investigates five-dimensional Lifshitz gauge theories with z=2 scaling, exploring their quantum properties, symmetry constraints, and potential for supersymmetry and symmetry enhancement at RG fixed points.

Contribution

It extends previous work by including matter in Lifshitz gauge theories and demonstrates possible symmetry enhancements at RG fixed points.

Findings

No-go theorems prevent spinorial supersymmetry and boost symmetry without constraints.

RG flows can lead to fixed points with supersymmetry and super-Schrodinger symmetry.

Examples of Lifshitz gauge theories with scalar supersymmetry are provided.

Abstract

Lagrangian gauge theories with a z=2 Lifshitz scaling provide a family of interacting, asymptotically free five-dimensional field theories. We examine some of their quantum properties, extending previous results to include matter. We present no-go theorems that, in the absence of constraints, such theories cannot admit a spinorial supersymmetry or a boost symmetry. However, we argue that there exist renormalization group flows whose fixed points can admit supersymmetry and boosts, i.e. super-Schrodinger symmetry. We also present examples of Lifshitz gauge theories with a scalar supersymmetry.