Vacuum polarization and induced Maxwell and Kalb-Ramond effective action in very special relativity

Abstract

This work investigates the implications of very special relativity (VSR) on the calculation of vacuum polarization for fermions in the presence of Maxwell and Kalb-Ramond gauge fields in four-dimensional spacetime. We derive the $SIM(2)$-covariant gauge theory associated with an Abelian antisymmetric 2-tensor and its corresponding field strength. We demonstrate that the free VSR-Kalb-Ramond electrodynamics is equivalent to a massive scalar field with a single polarization. Furthermore, we determine an explicit expression for the effective action involving Maxwell and Kalb-Ramond fields due to fermionic vacuum polarization at one-loop order. The quantum corrections generate divergences free of nonlocal terms only in the VSR-Maxwell sector. At the same time, we observe UV/IR mixing divergences due to the entanglement of VSR-nonlocal effects with quantum higher-derivative terms for the Kalb-Ramond field. However, in the lower energy limit, the effective action can be renormalized like in the Lorentz invariant case.

arXiv comment26 pages, 3 figures

References in corpus (42)

• Lorentz-Violating Extension of the Standard Model
• Very Special Relativity
• General Very Special Relativity is Finsler Geometry
• Lorentz violation with an antisymmetric tensor
• The General Very Special Relativity in Finsler Cosmology
• Modified black hole solution with a background Kalb-Ramond field
• Very special relativity as relativity of dark matter: the Elko connection
• A Realization of the Cohen-Glashow Very Special Relativity
• SIM(2)-invariant Modifications of Electrodynamic Theory
• Non Abelian Fields in Very Special Relativity
• Sim(2) and SUSY
• Very Special Relativity in Curved Space-Times
• Exact solution for a traversable wormhole in a curvature-coupled antisymmetric background field
• Antisymmetric tensor propagator with spontaneous Lorentz violation
• Kalb-Ramond field localization on the Bloch brane
• Renormalizability of the Dynamical Two-Form
• On the photon mass in Very Special Relativity
• Bianchi type I cosmology with a Kalb-Ramond background field
• Spontaneous Breaking of Lorentz Symmetry with an antisymmetric tensor
• Noncommutative Spacetime in Very Special Relativity
• Dirac equation in very special relativity for hydrogen atom
• A $Sim(2)$ invariant dimensional regularization
• Spin dependent masses and Sim(2) symmetry
• Anomalous Gauge Theories with Antisymmetric Tensor Fields
• Very Special Relativity and Lorentz Violating Theories
• Mandelstam-Leibbrandt prescription
• On the dual equivalence of the self-dual and topologically massive $B\wedge F$ models coupled to dynamical fermionic matter
• Localization of abelian gauge fields with Stueckelberg-like geometrical coupling on $f(T,B)$-thick brane
• Reducible gauge theories in very special relativity
• Quantum field theory with a preferred direction: The very special relativity framework
• Axion Mass Bound in Very Special Relativity
• Very Special Linear Gravity: A Gauge-Invariant Graviton Mass
• Dirac neutrino mass from the beta decay end-point modified by the dynamics of a Lorentz-violating equation of motion
• Vacuum polarisation induced coupling between Maxwell and Kalb-Ramond Fields
• SIM$(1)$--VSR Maxwell-Chern-Simons electrodynamics
• Induced Maxwell-Chern-Simons Effective Action in Very Special Relativity
• Dual equivalence between self-dual and topologically massive $B\wedge F$ models coupled to matter in $3+1$ dimensions
• Induced non-Abelian Chern-Simons effective action in very special relativity
• Superfield Effective Potential for the 2-form field
• Corrections to the Gyromagnetic Factor in Very Special Relativity
• Dualization between supersymmetric self-dual and topologically massive models coupled to matter in four-dimensional superspace
• $\beta$-function for topologically massive gluons