Dimensional Reduction of the Abelian-Higgs Carroll-Field-Jackiw Model

TL;DR

This paper reduces a Lorentz-violating Abelian-Higgs model from 3+1 to 2+1 dimensions, analyzing its propagators, dispersion relations, causality, and unitarity, and demonstrating its consistency in the lower dimension.

Contribution

It introduces a novel planar model derived from a Lorentz-violating 4D Abelian-Higgs theory, with detailed analysis of its physical properties.

Findings

Model is causal and unitary at tree-level.

Propagators and dispersion relations are explicitly calculated.

Lorentz violation is incorporated via a fixed background vector.

Abstract

Taking as a starting point a Lorentz non-invariant Abelian-Higgs model defined in 1+3 dimensions, we carry out its dimensional reduction to D=1+2, obtaining a new planar model composed by a Maxwell-Chern-Simons-Proca gauge sector, a massive scalar sector, and a mixing term (involving the fixed background (v^{\mu}) that imposes the Lorentz violation to the reduced model. The propagators of the scalar and massive gauge field are evaluated and the corresponding dispersion relations determined. Based on the poles of the propagators, a causality and unitarity analysis is carried out at tree-level. One then shows that the model is totally causal and unitary.