Novel discrete symmetries in the general N = 2 supersymmetric quantum mechanical model

TL;DR

This paper demonstrates that the N=2 supersymmetric quantum mechanical model exhibits novel discrete symmetries linked to Hodge duality, establishing it as a physical realization of Hodge theory with implications for differential geometry.

Contribution

It introduces new discrete symmetries in N=2 SUSY quantum mechanics and proves these models embody Hodge theory through symmetry transformations.

Findings

Discrete symmetries correspond to Hodge duality

SUSY transformations realize de Rham cohomological operators

Model exemplifies Hodge theory in physics

Abstract

In addition to the usual supersymmetric (SUSY) continuous symmetry transformations for the general N = 2 SUSY quantum mechanical model, we show the existence of a set of novel discrete symmetry transformations for the Lagrangian of the above SUSY quantum mechanical model. Out of all these discrete symmetry transformations, a unique discrete transformation corresponds to the Hodge duality operation of differential geometry and the above SUSY continuous symmetry transformations (and their anticommutator) provide the physical realizations of the de Rham cohomological operators of differential geometry. Thus, we provide a concrete proof of our earlier conjecture that any arbitrary N= 2 SUSY quantum mechanical model is an example of a Hodge theory where the cohomological operators find their physical realizations in the language of symmetry transformations of this theory. Possible physical implications of our present study are pointed out, too.