A Free N = 2 Supersymmetric System: Novel Symmetries

TL;DR

This paper uncovers new discrete symmetries in a free N=2 supersymmetric quantum system, linking them to differential geometry concepts and demonstrating the model's role as a tractable example of Hodge theory.

Contribution

It introduces novel discrete symmetries in a free N=2 SUSY system and connects them to differential geometric operators, expanding understanding of supersymmetric models.

Findings

Identification of novel discrete symmetries in N=2 SUSY system

Connection between symmetries and de Rham cohomological operators

Demonstration of the model as a realization of Hodge theory

Abstract

We discuss a set of novel discrete symmetries of a free N = 2 supersymmetric (SUSY) quantum mechanical system which is the limiting case of a widely-studied interacting SUSY model of a charged particle constrained to move on a sphere in the background of a Dirac magnetic monopole. The usual continuous symmetries of this model provide the physical realization of the de Rham cohomological operators of differential geometry. The interplay between the novel discrete symmetries and usual continuous symmetries leads to the physical realization of relationship between the (co-)exterior derivatives of differential geometry. We have also exploited the supervariable approach to derive the nilpotent N = 2 SUSY symmetries of the theory and provided the geometrical origin and interpretation for the nilpotency property. Ultimately, our present study (based on innate symmetries) proves that our free N = 2 SUSY example is a tractable model for the Hodge theory.