A Specific N = 2 Supersymmetric Quantum Mechanical Model: Supervariable Approach

TL;DR

This paper derives off-shell nilpotent supersymmetry transformations for a specific N=2 supersymmetric quantum mechanical model using supervariable approach, providing geometric insights and linking it to Hodge theory.

Contribution

It introduces a supervariable method to obtain supersymmetry transformations and explores their geometric interpretation in a specific N=2 SUSY quantum mechanics model.

Findings

Derived off-shell nilpotent symmetry transformations.

Provided geometric interpretation of the transformations.

Linked the model to Hodge theory.

Abstract

By exploiting the supersymmetric invariant restrictions on the chiral and anti-chiral supervariables, we derive the off-shell nilpotent symmetry transformations for a specific (0 + 1)-dimensional N = 2 supersymmetric quantum mechanical model which is considered on a (1, 2)-dimensional supermanifold (parametrized by a bosonic variable t and a pair of Grassmannian variables (\theta, \bar\theta). We also provide the geometrical meaning to the symmetry transformations. Finally, we show that this specific N = 2 SUSY quantum mechanical model is a model for Hodge theory.