Coupled $\mathcal{N}$ = 2 supersymmetric quantum systems: symmetries and supervariable approach

TL;DR

This paper explores $ abla$ = 2 supersymmetric quantum systems, identifying multiple discrete symmetries linked to Hodge duality, and extends the analysis to more general models using supervariable methods.

Contribution

It demonstrates the existence of multiple discrete symmetries as Hodge duals and introduces a supervariable approach to derive on-shell nilpotent symmetries in $ abla$ = 2 models.

Findings

Identification of two sets of discrete symmetries related to Hodge duality

Proof supporting multiple discrete symmetries as Hodge duals

Extension of analysis to general models using supervariable approach

Abstract

We consider specific examples of $\mathcal{N}$ = 2 supersymmetric quantum mechanical models and list out all the novel symmetries. In each case, we show the existence of two sets of discrete symmetries that correspond to the Hodge duality operator of differential geometry. Thus, we are able to provide a proof of the conjecture which endorses the existence of more than one discrete symmetry transformation as the analogue of Hodge duality operation. Finally, we extend our analysis to a more general case and derive on-shell nilpotent symmetries within the framework of supervariable approach.