Dimensional Reduction of a Lorentz and CPT-violating Maxwell-Chern-Simons Model

TL;DR

This paper explores the dimensional reduction of a Lorentz and CPT-violating Maxwell-Chern-Simons model from 3+1 to 2+1 dimensions, analyzing its stability, causality, and unitarity properties in the reduced planar setting.

Contribution

It introduces a new planar model derived from a higher-dimensional Lorentz and CPT-violating theory, analyzing its physical consistency and symmetry properties.

Findings

The reduced model maintains stability.

Causality may be compromised by certain modes.

Gauge sector remains unitary under all conditions.

Abstract

Taking as starting point a Lorentz and CPT non-invariant Chern-Simons-like model defined in 1+3 dimensions, we proceed realizing its dimensional reduction to D=1+2. One then obtains a new planar model, composed by the Maxwell-Chern-Simons (MCS) sector, a Klein-Gordon massless scalar field, and a coupling term that mixes the gauge field to the external vector, $v^{\mu}$. In spite of breaking Lorentz invariance in the particle frame, this model may preserve the CPT symmetry for a single particular choice of $v^{\mu}$. Analyzing the dispersion relations, one verifies that the reduced model exhibits stability, but the causality can be jeopardized by some modes. The unitarity of the gauge sector is assured without any restriction, while the scalar sector is unitary only in the space-like case. PACS numbers: 11.10.Kk; 11.30.Cp; 11.30.Er; 12.60.-i