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arXiv · 2306.14309

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

Roberto V. Maluf·Gonzalo J. Olmo
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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.

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Roberto V. Maluf, Gonzalo J. Olmo. 2023-06-25. Vacuum polarization and induced Maxwell and Kalb-Ramond effective action in very special relativity. https://doi.org/10.1103/physrevd.108.095022

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