Revisiting Novel Symmetries in Coupled $\mathcal{N} = 2$ Supersymmetric Quantum Systems: Examples and Supervariable Approach

TL;DR

This paper explores new symmetries in $ abla$ = 2 supersymmetric quantum systems, demonstrating their connection to Hodge duality and deriving on-shell nilpotent symmetries using supervariable methods.

Contribution

It identifies multiple discrete symmetries linked to Hodge duality and extends the analysis to a general coupled system, providing a proof of their existence.

Findings

Existence of two sets of discrete symmetries related to Hodge duality.

Proof of multiple discrete symmetry transformations in $ abla$ = 2 SUSY QM.

Derivation of on-shell nilpotent symmetries for generalized superpotentials.

Abstract

We revisit the novel symmetries in $\mathcal{N}$ = 2 supersymmetric (SUSY) quantum mechanical (QM) models by considering specific examples of coupled systems. Further, we extend our analysis to a general case 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 points out the existence of more than one set of discrete symmetry transformations corresponding to the Hodge duality operator. Moreover, we derive on-shell nilpotent symmetries for a generalized superpotential within the framework of supervariable approach.