Planar anisotropic CPT-odd systems: A field theoretical approach

The primary objective of this study is to introduce field-theoretical tools into the realm of physical properties within planar systems exhibiting possible anisotropic features. This goal is achieved by fitting a specific field-theoretical model to simulate the presence of such a system. The proposed approach enables the investigation of in-plane physical phenomena using analytic methods. Specifically, our focus is on phenomena related to stationary point-like field sources that can mimic defects in material layers. We employ a dimensional reduction procedure on the well-known Carroll–Field–Jackiw model to derive a planar theory. This theory includes an electromagnetic sector governed by Maxwell-Chern–Simons electrodynamics, a scalar sector described by a massless Klein–Gordon field, and a mixed sector where the background vector controls the interactions between the scalar and gauge fields. Across all sectors of this planar theory, we explore physical phenomena arising from interactions with external sources. Specifically, we analyze perturbative effects up to second order in the background vector, examining contributions from both electric and scalar planar charges as well as Dirac points.