Novel symmetries in N = 2 supersymmetric quantum mechanical models

TL;DR

This paper uncovers new discrete symmetries in N=2 supersymmetric quantum mechanics models, linking them to Hodge duality and suggesting their role as models for Hodge theory.

Contribution

It identifies novel discrete symmetries in N=2 SUSY quantum mechanics and connects these to de Rham cohomology and Hodge duality, expanding the understanding of supersymmetric models.

Findings

Discovery of new discrete symmetries in N=2 SUSY models

Connection of symmetries to Hodge duality operations

Proposal that all N=2 SUSY systems can model Hodge theory

Abstract

We demonstrate the existence of a novel set of discrete symmetries in the context of N = 2 supersymmetric (SUSY) quantum mechanical model with a potential function f(x) that is a generalization of the potential of the 1D SUSY harmonic oscillator. We perform the same exercise for the motion of a charged particle in the X-Y plane under the influence of a magnetic field in the Z-direction. We derive the underlying algebra of the existing continuous symmetry transformations (and corresponding conserved charges) and establish its relevance to the algebraic structures of the de Rham cohomological operators of differential geometry. We show that the discrete symmetry transformations of our present general theories correspond to the Hodge duality operation. Ultimately, we conjecture that any arbitrary N = 2 SUSY quantum mechanical system can be shown to be a tractable model for the Hodge theory.