Duality in $SIM(2)$ topologically massive models with $B\wedge F$ term

TL;DR

This work extends the classical duality between self-dual and topologically massive gauge theories to a $SIM(2)$-invariant, $3+1$-dimensional setting within Very Special Relativity. By combining a direct equations-of-motion comparison with a master Lagrangian approach, the authors show that the duality between the $SIM(2)$-invariant SD model with a $B\wedge F$ term and the $SIM(2)$ Maxwell–Kalb–Ramond theory persists, while acquiring nonlocal corrections characteristic of VSR. When fermionic matter is included, a Thirring-like interaction emerges in the MKR sector, with nonlocal VSR modifications reflected in the boson–fermion mapping. Overall, the results generalize known Lorentz-invariant dualities to the VSR framework and illuminate how nonlocality modifies gauge-duality structures without introducing extra degrees of freedom.

Abstract

This paper aims to investigate the classical duality between the $SIM(2)$-Maxwell-Kalb-Ramond (MKR) theory and a self-dual non-gauge-invariant model. First, we establish the equivalence in the free-field case using two complementary methods: a direct comparison of the equations of motion and the master Lagrangian approach. In both methodologies, we verify that the classical correspondence between the MKR model and self-dual fields exhibits modifications induced by very special relativity (VSR). Moreover, we employ the master Lagrangian approach to examine the duality when the self-dual model is minimally coupled to fermionic matter. We show that the resulting MKR model contains Thirring-like interactions modified by nonlocal contributions arising from VSR.