Killing-Yano Cotton currents

We discuss conserved currents constructed from the Cotton tensor and (conformal) Killing-Yano tensors (KYTs). consider corresponding charges generally then exemplify with four-dimensional Pleba\'nski-Demia\'nski metric where they are proportional to sum of squares electric magnetic charges. As part derivation, we also find two conformal in recently introduced coordinates Podolsky Vratny. The construction asymptotic for current is elucidated compared three-dimensional Topologically Massive Gravity. For case, give a superspace multiplet that contains bosonic sector. In mathematical section, derive potentials currents, identities KYTs torsionful backgrounds.