# Schwinger Model \`a la Very Special Relativity

## TL;DR

This paper explores how Very Special Relativity (VSR) influences the Schwinger model in 1+1 dimensions, revealing modifications in current conservation, anomalies, and the introduction of VSR-inspired mass terms.

## Contribution

It demonstrates the incorporation of VSR-inspired terms into the Schwinger model, analyzing their effects on currents and anomalies in a lower-dimensional setting.

## Key findings

- Axial current remains classically conserved with VSR mass terms.
- Both vector and axial currents are modified by nonlocal operators in electromagnetic fields.
- The axial anomaly retains its topological nature but with a modified coefficient.

## Abstract

In this work, we show that Lorentz invariant theories in $1+1$ dimensions admit new terms inspired by Very Special Relativity (VSR) theories. We have studied the Schwinger model in VSR. We show the axial current is classically conserved in the presence of a mass term coming from the VSR invariant terms but without standard Lorentz invariant mass. Furthermore, it is shown that both the vector current as well as the axial current are modified with respect to the free case when the fermion is coupled to an external electromagnetic field due to the nonlocal operator present in the theory. The axial anomaly is computed, and we found the same standard topological invariant with a modification in the coefficient.