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.