Gauged Lifshitz scalar field theories in two dimensions

TL;DR

This paper develops two-dimensional gauged Lifshitz scalar field theories, exploring duality relations and gauge invariance, and connects them to the well-known Schwinger model while addressing anomalies and consistency.

Contribution

It introduces new gauged Lifshitz scalar models in two dimensions, analyzing duality relations, anomalies, and gauge invariance, extending the understanding of such theories beyond the standard models.

Findings

Partial duality recovers the bosonized Schwinger model in IR limit.

Exact duality leads to non-conserved source current and anomalies.

Adding Wess-Zumino action maintains gauge invariance in the model.

Abstract

We present two-dimensional gauged Lifshitz scalar field theories by considering the duality relation between the source current and the Noether current. Requiring the duality partially, we obtain a gauged model which recovers the bosonized Schwinger model for the IR limit. For the exact duality, however, the source current is not conserved, which means that the resulting theory is anomalous, so that the number of degrees of freedom is increased. The second model is consistently formulated by adding the Wess-Zumino type action to maintain the gauge invariance.