Photon sector analysis of Super and Lorentz symmetry breaking: effective photon mass, bi-refringence and dissipation
Within the Standard Model Extension (SME), we expand our previous findings on four classes of violations of Super-Symmetry (SuSy) and Lorentz Symmetry (LoSy), differing in the handedness of the Charge conjugation-Parity-Time reversal (CPT) symmetry and in whether considering the impact of photinos on photon propagation. The violations, occurring at the early universe high energies, show visible traces at present in the Dispersion Relations (DRs). For the CPT-odd classes ($V_μ$ breaking vector) associated with the Carroll-Field-Jackiw (CFJ) model, the DRs and the Lagrangian show for the photon an effective mass, gauge invariant, proportional to $|{\vec V}|$. The group velocity exhibits a classic dependency on the inverse of the frequency squared. For the CPT-even classes ($k_{F}$ breaking tensor), when the photino is considered, the DRs display also a massive behaviour inversely proportional to a coefficient in the Lagrangian and to a term linearly dependent on $k_{F}$. All DRs display an angular dependence and lack LoSy invariance. In describing our results, we also point out the following properties: i) the appearance of complex or simply imaginary frequencies and super-luminal speeds and ii) the emergence of bi-refringence. Finally, we point out the circumstances for which SuSy and LoSy breakings, possibly in presence of an external field, lead to the non-conservation of the photon energy-momentum tensor. We do so for both CPT sectors.