Interactions Between Charges in a Planar Model in the Presence of Nonminimal Lorentz Violation

Even if Lorentz symmetry is not a fundamental property of condensed matter physics, there are many instances where the relevant physics of some material is well described by a relativistic field theory. Actually, in some cases, this effective description is not of an exact Lorentz invariant model, but of a model including some small Lorentz-violating correction. In this case, a connection can be made between condensed matter physics and the Standard Model Extension (SME) that have been developed to look for Lorentz violation in fundamental physics. We are interested in particular in the connection between the SME and planar physics. We study the connection between part of the non-minimal SME and a planar model, and we calculate the interaction energies and torques appearing between point-like charges in the planar model. We show how the dimensional reduction leads to new sectors appearing in the planar theory and that the interplay between those sectors can lead to very distinctive phenomena.