Anomalous function of a Lorentz-violating QED effective action and the relation between compact bulk scalar propagator and path integral duality

TL;DR

This paper investigates Lorentz violation in a 5D compact spacetime, calculating an anomalous function in QED, and finds a connection between bulk scalar propagator and path integral duality, offering new insights into Lorentz symmetry breaking.

Contribution

It introduces a novel calculation of a Lorentz-violating term in 4D QED effective action using path integrals and links Lorentz violation due to compactification with path integral duality.

Findings

Lorentz invariance is broken by compactification in 5D spacetime.

The anomalous function of Lorentz-violating term is explicitly calculated.

Bulk scalar propagator aligns with path integral duality, revealing a new perspective.

Abstract

In this paper, we consider a compact five dimensional spacetime with the structure $\mathcal{M}^{1,3}\times S^{1}$. Generally speaking, motion on such a structure will break Lorentz invariance, allowing for causal bulk signals to propagate superluminally. Based on recent articles, we calculate the anomalous function of a gauge invariant but Lorentz-violating term in the $4D$ QED effective action by using path integral. Finally, we find that the compact bulk scalar propagator and path integral duality are consistent, this result brings a new perspective: the behavior of breaking Lorentz invariance caused by dimensional compactness can be seen as path integral duality.