Killing-Yano Cotton Currents

2021-10-07

Authors: Ulf Lindström and Özgür Sariıoğlu

Preprint number: UUITP-48/21

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