Aharonov-Bohm effect on AdS_2 and nonlinear supersymmetry of reflectionless Poschl-Teller system

TL;DR

This paper explores how the Aharonov-Bohm effect influences nonlinear supersymmetry in a reflectionless Poschl-Teller system on AdS_2, revealing connections to holography and discrete symmetries.

Contribution

It uncovers the origin of nonlinear supersymmetry in the Poschl-Teller system via the Aharonov-Bohm effect on AdS_2 and highlights the role of discrete symmetries and holographic correspondence.

Findings

Aharonov-Bohm effect explains supersymmetry origin.

Discrete symmetries relate to space and time reflections.

Holographic-like correspondence observed between systems.

Abstract

We explain the origin and the nature of a special nonlinear supersymmetry of a reflectionless Poschl-Teller system by the Aharonov-Bohm effect for a nonrelativistic particle on the AdS_2. A key role in the supersymmetric structure appearing after reduction by a compact generator of the AdS_2 isometry is shown to be played by the discrete symmetries related to the space and time reflections in the ambient Minkowski space. We also observe that a correspondence between the two quantum non-relativistic systems is somewhat of the AdS/CFT holography nature.