Novel symmetries in an interacting N = 2 supersymmetric quantum mechanical model

TL;DR

This paper uncovers new discrete symmetries in an interacting N=2 supersymmetric quantum mechanical model, linking them to differential geometry and providing geometric interpretations of supersymmetry transformations and invariants.

Contribution

It introduces novel discrete symmetries in an N=2 SUSY quantum system and interprets them within differential geometry, along with deriving SUSY transformations via a supervariable approach.

Findings

Discovery of new discrete symmetries in the model

Geometrical interpretation of SUSY transformations

Expression of supercharges and invariance in supervariable language

Abstract

We demonstrate the existence of a set of novel discrete symmetry transformations in the case of an interacting N = 2 supersymmetric quantum mechanical model of a system of an electron moving on a sphere in the background of a magnetic monopole and establish its interpretation in the language of differential geometry. These discrete symmetries are, over and above, the usual three continuous symmetries of the theory which together provide the physical realizations of the de Rham cohomological operators of differential geometry. We derive the nilpotent N = 2 SUSY transformations by exploiting our idea of supervariable approach and provide geometrical meaning to these transformations in the language of Grassmannian translational generators on a (1, 2)-dimensional supermanifold on which our N = 2 SUSY quantum mechanical model is generalized. We express the conserved supercharges and the invariance of the Lagrangian in terms of the supervariables (obtained after the imposition of the SUSY invariant restrictions) and provide the geometrical meaning to (i) the nilpotency property of the N = 2 supercharges, and (ii) the SUSY invariance of the Lagrangian of our N = 2 SUSY theory.