In this work, we investigate the consequences of the spontaneous breaking of Lorentz symmetry, triggered by the bumblebee vector field, on the usual Einstein-Hilbert theory. Specifically, we consider the Einstein-Hilbert action modified by the bumblebee dynamic field, and evaluate the graviton propagator using an extended basis of Barnes-Rivers tensor projectors, involving the Lorentz-violating vector. Once the propagator is carried out, we proceed with discussing the consistency of the model, writing the dispersion relations, and analyzing causality and unitarity. We verify that this model possesses two dispersion relations: one provides causal and unitary propagating modes, while the second one yields a causal but nonunitary mode which spoils the physical consistency of the model.

In this work we study how $CPT$-odd Maxwell-Carroll-Field-Jackiw (MCFJ) electrodynamics as well as a dimension-5 extension of it affect the optical activity of continuous media. The starting point is dimension-3 MCFJ electrodynamics in matter whose modified Maxwell equations, permittivity tensor, and dispersion relations are recapitulated. Corresponding refractive indices are achieved in terms of the frequency and the vector-valued background field. For a purely timelike background, the refractive indices are real. Their associated propagation modes are circularly polarized and exhibit birefringence. For a purely spacelike background, one refractive index is always real and the other can be complex. The circularly polarized propagating modes may exhibit birefringence and dichroism (associated with absorption). Subsequently, we examine a dimension-five MCFJ-type electrodynamics, previously scrutinized in the literature, in a continuous medium. Following the same procedure, we find the refractive indices from a sixth-order dispersion equation. For a purely timelike background, three distinct refractive indices are obtained, one of them being real and two being complex. They are associated with two circularly polarized propagating modes that exhibit birefringence or dichroism, depending on the frequency range. Scenarios of propagation and absorption analogous to those found in dispersive dielectrics are also observed for purely spacelike background configurations. We conclude by comparing the dimension-three and five results and by emphasizing the richer phenomenology of the propagating modes in the higher-derivative model. Our results are applicable in the realm of Weyl semimetals.

We analyze some dimension-five $CPT$-even and Lorentz-violating nonminimal couplings between fermionic and gauge fields in the context of the Dirac equation. After evaluating the nonrelativistic Hamiltonian, we discuss the behavior of the terms under discrete symmetries and analyze the implied effects. We then use the anomalous magnetic dipole moment and electron electric dipole moment measurements to reach upper bounds of 1 part in ${10}^{20}$ and ${10}^{24}(\mathrm{eV}{)}^{-1}$, improving the level of restriction on such couplings by at least 8 orders of magnitude. These upper bounds are also transferred to the Sun-centered frame by considering the Earth’s rotational motion.

We study BPS vortices in a CPT-odd and Lorentz-violating Maxwell–Chern–Simons–Higgs (MCSH) electrodynamics attained from the dimensional reduction of the Carroll–Field–Jackiw–Higgs model. The...

In this paper, we investigate an electrodynamics in which the physical modes are coupled to a Lorentz-violating background by means of a higher-derivative term. We analyze the modes associated with the dispersion relations obtained from the poles of the propagator. More specifically, we study Maxwell’s electrodynamics modified by a Lorentz-violating operator of mass dimension 6. The modification has the form $D_{\beta \alpha }{\partial }_{\sigma }{F}^{\sigma \beta }{\partial }_{\lambda }{F}^{\lambda \alpha }$; i.e., it possesses two additional derivatives coupled to a $CPT$-even tensor $D_{\beta \alpha }$ that plays the role of the fixed background. We first evaluate the propagator and obtain the dispersion relations of the theory. By doing so, we analyze some configurations of the fixed background and search for sectors where the energy is well defined and causality is assured. A brief analysis of unitarity is included for particular configurations. Afterward, we perform the same kind of analysis for a more general dimension-6 model. We conclude that the modes of both Lagrange densities are possibly plagued by physical problems, including causality and unitarity violation, and that signal propagation may become physically meaningful only in the high-momentum regime.