Hidden superconformal symmetry: Where does it come from?

TL;DR

This paper reveals the origin of hidden superconformal symmetry in quantum systems by applying a nonlocal transformation to extended systems with fermions, uncovering different mechanisms for its emergence.

Contribution

It demonstrates how nonlocal Foldy-Wouthuysen transformations can derive hidden superconformal symmetry from various extended fermionic systems.

Findings

Hidden superconformal symmetry can be derived from extended systems with fermions.

Different systems generate the symmetry through distinct mechanisms.

The symmetry of the free particle system emerges in the zero-frequency limit.

Abstract

It is known that a single quantum harmonic oscillator is characterized by a hidden spectrum generating superconformal symmetry, but its origin has remained rather obscure. We show how this hidden superconformal symmetry can be derived by applying a nonlocal Foldy-Wouthuysen transformation to three extended systems with fermion degrees of freedom. The associated systems have essentially different nature from the point of view of conventional supersymmetric quantum mechanics, and generate the desired hidden symmetry in three different ways. We also trace out how the hidden superconformal symmetry of the quantum free particle system is produced in the limit of zero frequency.