Aharonov–Bohm effect on AdS2 and nonlinear supersymmetry of reflectionless Pöschl–Teller system

We explain the origin and the nature of a special nonlinear supersymmetry of a reflectionless Pöschl–Teller system by the Aharonov–Bohm effect for a non-relativistic particle on the AdS2. A key role in the supersymmetric structure appearing after reduction by a compact generator of the AdS2 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.