Aharonov--Casher effect from a supersymmetric N=1 D=4 model with Kalb--Ramond Lorentz-violating background: a SUSY-preserving mechanism via the Fayet--Iliopoulos term

Abstract

The Aharonov--Casher (AC) effect describes the geometric phase acquired by a neutral particle carrying a magnetic dipole moment moving in an external electric field. In supersymmetric gauge theories it is often argued that exact supersymmetry enforces the vanishing of anomalous magnetic dipole moments, suggesting that the AC interaction may be incompatible with unbroken supersymmetry in four dimensions. In this work we show that this conclusion is model-dependent. We construct an $N=1$, $D=4$ supersymmetric gauge model in which a Lorentz-violating Kalb--Ramond background induces dynamically the dipole interaction responsible for the AC effect while leaving the supersymmetry algebra intact. The model couples a chiral superfield to an Abelian gauge superfield through a Chern--Simons--type interaction supplemented by a Fayet--Iliopoulos term. A duality identification between the symmetric combination $S+S^\dagger$ of the chiral superfield and the Kalb--Ramond superfield strength allows the antisymmetric tensor background to enter the supersymmetric dynamics without breaking supersymmetry. Integrating out the auxiliary $D$ field generates dynamically an effective dipole interaction of the form $\bar{\psi}\sigma^{\mu\nu}F_{\mu\nu}\psi$. In the nonrelativistic limit the resulting equation of motion reproduces the Aharonov--Casher Hamiltonian for a neutral fermion. The effective magnetic dipole moment is expressed in terms of the parameters of the model and can be mapped onto tensor coefficients of the fermion sector of the Standard Model Extension. Our results therefore provide an explicit realization of a four-dimensional supersymmetric theory in which the Aharonov--Casher interaction emerges dynamically while supersymmetry remains exact in the presence of Lorentz violation.