Hidden supersymmetries in supersymmetric quantum mechanics

TL;DR

This paper explores hidden supersymmetries in simple supersymmetric quantum mechanics models, emphasizing the role of Lie algebra cohomology and geometric mechanisms in their emergence.

Contribution

It identifies the conditions under which hidden supersymmetries appear, linking them to invariant tensors and algebraic cohomology properties.

Findings

Hidden supersymmetries depend on odd order invariant tensors.

Existence of hidden supersymmetries is linked to Lie algebra cohomology.

Geometrical mechanisms can induce additional supersymmetries.

Abstract

We discuss the appearance of additional, hidden supersymmetries for simple 0+1 $Ad(G)$-invariant supersymmetric models and analyse some geometrical mechanisms that lead to them. It is shown that their existence depends crucially on the availability of odd order invariant skewsymmetric tensors on the (generic) compact Lie algebra $\cal G$, and hence on the cohomology properties of the Lie algebra considered.