Dimensional reduction of theCPT-even electromagnetic sector of the standard model extension

Abstract

The CPT-even abelian gauge sector of the Standard Model Extension is represented by the Maxwell term supplemented by (KF ) µνρσ F µν F ρσ , where the Lorentz-violating background tensor, (KF ) µνρσ , 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.

Aspects of a planar nonbirefringent andCPT-even electrodynamics stemming from the standard model extension

“…This planar model possesses nine independent LV components including six parity-even and three parity-odd, being more simpler than the one of Ref. [28], in which the Lorentz-violation is governed by 19 parameters (see Lagrangian (1)). …”

“…A CPT-even field theory in (1+2)-dimensions model with Lorentz violation was recently attained by means of the dimensional reduction of the CPT-even gauge sector of the Standard Model Extension [28]. The resulting planar electrodynamics is composed of a gauge and scalar sectors, both endowed with Lorentz violation, whose planar Lagrangian is…”

“…[28]. In this simpler framework, Lorentz violation is controlled only by a rank-2, which modifies the kinetic part of the scalar and gauge sectors, and a rank-1 tensor, which couples both sectors.…”

“…[28], having shown that the pure abelian gauge or electromagnetic sector presents nonbirefringence at any order. The birefringence in this model is associated with the elements of the coupling tensor, T µλκ .…”

On the duality in CPT-even Lorentz-breaking theories

“…The Standard Model Extension (SME) [21][22][23][24], which provides a description of Lorentz and CPT violation in quantum field theories, also includes CPT-even terms. These CPT-even relativity-breaking models have been the focus of intense investigation recently and many issues related to classical solutions in these theories have been discussed (a very incomplete list is given in [25][26][27][28][29][30][31]). However, the dualization of CPT-even Lorentz-violating models has not been given much attention.…”