Hidden Supersymmetries of Deformed Supersymmetric Mechanics

TL;DR

This paper explores quantum models of deformed supersymmetric harmonic oscillators with arbitrary even supersymmetry, revealing hidden supersymmetries that explain energy degeneracies.

Contribution

It introduces new models based on worldline realizations of supergroups and uncovers hidden supersymmetries in these systems.

Findings

Models exhibit hidden SU(N/2|2) supersymmetry

Energy level degeneracies correspond to hidden symmetry representations

Constructs applicable for arbitrary even N supersymmetry

Abstract

We consider quantum models corresponding to superymmetrizations of the two-dimensional harmonic oscillator based on worldline $d=1$ realizations of the supergroup SU$(\,{\cal N}/2\,|1)$, where the number of supersymmetries ${\cal N}$ is arbitrary even number. Constructed models possess the hidden supersymmetry SU$(\,{\cal N}/2\,|2)$. Degeneracies of energy levels are spanned by representations of the hidden supersymmetry group.