Comments on the hidden symmetries of the spinning point particle in Kerr-Newman, D = 5 minimal gauged supergravity and higher dimensional spacetimes with Killing-Yano torsion

We investigate the hidden symmetries of the Kerr-Newman, of the D=5 minimal gauged supergravity which admits a Killing-Maxwell system in the sense of Carter and of higher dimensional spacetimes in the presence of Killing-Yano torsion. We note that when an electromagnetic tensor is present and an associated Killing-Maxwell system can be constructed in the sense of Carter, the Killing- Maxwell field becomes a PCKY (primary conformal Killing-Yano) tensor or a PGCKY (primary generalized conformal Killing-Yano) tensor, the latter in the presence of torsion. We point out the structure of the Dirac-type operators of the spinning point particle in arbitrary- dimensional spacetimes with torsion, focusing on the case when torsion can be assimilated with a Killing-Yano tensor and these spacetimes are endowed with towers of Killing-Yano tensors, and hence we show the anomalies of these additional supersymmetries cancel out in this particular case.