Dimensional reduction of the CPT-even electromagnetic sector of the Standard Model Extension

TL;DR

This paper investigates a dimensionally reduced, Lorentz-violating planar electrodynamics model derived from the Standard Model Extension, analyzing its dispersion relations, birefringence effects, and field behavior.

Contribution

It introduces a new planar Lorentz-violating electrodynamics model with exact dispersion relations and analyzes the effects of Lorentz violation on field behavior and birefringence.

Findings

Six Lorentz-violating parameters do not cause birefringence at any order.

Birefringence appears only as a second order effect linked to coupling tensors.

Lorentz violation induces angular dependence in fields without changing asymptotic behavior.

Abstract

The CPT-even abelian gauge sector of the Standard Model Extension is represented by the Maxwell term supplemented by $(K_{F})_{\mu\nu\rho\sigma}F^{\mu\nu}F^{\rho\sigma}$, where the Lorentz-violating background tensor, $(K_{F})_{\mu\nu\rho\sigma}$, possesses the symmetries of the Riemann tensor. In the present work, we examine the planar version of this theory, obtained by means of a typical dimensional reduction procedure to $(1+2)$ dimensions. The resulting planar electrodynamics is composed of a gauge sector containing six Lorentz-violating coefficients, a scalar field endowed with a noncanonical kinetic term, and a coupling term that links the scalar and gauge sectors. The dispersion relation is exactly determined, revealing that the six parameters related to the pure electromagnetic sector do not yield birefringence at any order. In this model, the birefringence may appear only as a second order effect associated with the coupling tensor linking the gauge and scalar sectors.The equations of motion are written and solved in the stationary regime. The Lorentz-violating parameters do not alter the asymptotic behavior of the fields but induce an angular dependence not observed in the Maxwell planar theory.