Supersymmetric exploration of external field effects on spinning cosmic strings with Aharonov–Bohm interaction

We have conducted a supersymmetric analysis of the spacetime of a spinning cosmic string, focusing on the behavior of an electron in magnetic fields. Our study involves examining the Dirac system through the lens of exceptional orthogonal polynomials, specifically the exceptional orthogonal Laguerre $X_{m}$ polynomials. This analysis transforms the Dirac system into a relativistic system with a nonlinear isotonic oscillator. Additionally, we introduce new potential models that extend the radial oscillator by incorporating rational terms. Comprehensive analyses of the potential, energy levels, and probability density graphs are provided for various topological defects of cosmic strings and different parameters of the Aharonov-Bohm interaction. Recent studies on the quantum dynamics of fermions in the presence of topological defects, such as those by \cite{hassan} and \cite{silva2}, set the stage for the supersymmetric framework explored in this paper, which extends their results through a detailed analysis of exceptional orthogonal polynomials.