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

TL;DR

This paper explores the classical duality between $SIM(2)$-Maxwell-Kalb-Ramond theory and a self-dual model, revealing modifications due to very special relativity and nonlocal interactions when coupled to matter.

Contribution

It demonstrates the duality in the presence of VSR effects and extends the analysis to matter coupling, highlighting nonlocal modifications.

Findings

Duality verified via equations of motion and master Lagrangian methods

VSR induces modifications in the duality correspondence

Coupling to matter introduces nonlocal Thirring-like interactions

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.