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

TL;DR

This paper explores how very special relativity (VSR) modifies vacuum polarization effects for fermions interacting with Maxwell and Kalb-Ramond fields, deriving effective actions and analyzing quantum divergences and renormalization.

Contribution

It derives the VSR-covariant gauge theory for Abelian antisymmetric fields and computes the one-loop effective action, revealing unique divergence structures and renormalization properties.

Findings

VSR-Kalb-Ramond electrodynamics is equivalent to a massive scalar with one polarization.

Quantum corrections produce divergences only in the Maxwell sector, free of nonlocal terms.

UV/IR mixing divergences occur in the Kalb-Ramond sector due to VSR effects.

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.