Aspects of field theories with Lorentz symmetry violation

Abstract

In recent years, studies on Lorentz symmetry violation (LSV) in field theory have gained significant prominence in the literature. Such investigations have led to the construction of the Standard Model Extension (SME), which possesses both minimal and non-minimal versions. The minimal SME contains only renormalizable terms, whereas the non-minimal formulation includes all non-renormalizable operators. In this thesis, we investigate a variety of theoretical and phenomenological aspects of LSV within the frameworks of the SME, very special relativity (VSR), and related effective field theories, which employ background vector and tensor fields. In the first part of this work, we focus on aspects of LSV in flat spacetime, including one-loop radiative corrections and dualities. We begin by revisiting the gauge and fermionic sectors of Lorentz-violating (LV) quantum electrodynamics (QED) with CPT-odd and CPT-even terms. We show that the axial coupling 𝑏𝜇¯ 𝜓 𝛾𝜇𝛾5𝜓 induces coefficients that depend on the choice of regularization scheme and on the treatment of 𝛾5 in different dimensions. We also study radiative corrections in a vector model with spontaneous LSV, known in the literature as the bumblebee model. In addition to Lorentz symmetry breaking, this model exhibits gauge symmetry violation. To restore gauge symmetry, we introduce a Stueckelberg field and calculate the two-point function by employing the principal-value (PV) prescription. The result is non-transversal, leading to a massive excited mode. Furthermore, we investigate the classical duality between the 𝑆𝐼𝑀(1) - Maxwell-Chern-Simons (MCS) model and its self-dual counterpart. Initially, our analysis focuses on free-field cases in order to establish equivalence through two distinct approaches: comparison of the equations of motion and the use of the master Lagrangian method. Another topic addressed involves the classical duality between the 𝑆𝐼𝑀(2) - Maxwell-Kalb-Ramond (MKR) model and its non-gauge-invariant self-dual counterpart. We establish the equivalence for free-field theories by employing two methods: direct comparison of the equations of motion and the master Lagrangian approach. In both methodologies, the classical correspondence between the MKR model and self-dual fields exhibits modifications due to VSR. In the second part of the thesis, we examine aspects of LSV in curved spacetime, deriving a black hole solution with a global monopole in a modified gravity framework that includes a self-interacting Kalb-Ramond tensor field non-minimally coupled to gravity. Finally, the thesis discusses the phenomenological implications and experimental prospects of the studied models by establishing bounds on LV coefficients and comparing theoretical consistency conditions with current and future experimental sensitivities. The results presented here contribute to a deeper understanding of how LSV may manifest in field theories and gravitational contexts.