Killing-Yano Cotton Currents
arXiv:2110.03470 · doi:10.1007/JHEP03(2022)029
Abstract
We discuss conserved currents constructed from the Cotton tensor and (conformal) Killing-Yano tensors (KYTs). We consider the corresponding charges generally and then exemplify with the four-dimensional Plebański-Demiański 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 Plebański-Demiański 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.
arXiv comment20 pages; ver. 2: to appear in JHEP
References in corpus (28)
- The Black Hole in Three Dimensional Space Time
- A new look at the Plebanski-Demianski family of solutions
- SUSY in the sky
- Black holes, hidden symmetries, and complete integrability
- Energy in Topologically Massive Gravity
- Conformal supergravity in three dimensions: New off-shell formulation
- On conformal Killing-Yano tensors for Plebanski-Demianski family of solutions
- Mass and angular momentum of asymptotically AdS or flat solutions in the topologically massive gravity
- Properties of hyperkahler manifolds and their twistor spaces
- Conserved gravitational charges from Yano tensors
- Killing(-Yano) Tensors in String Theory
- Killing-Yano tensors and some applications
- New improved form of black holes of type D
- Killing-Yano Supersymmetry in String Theory
- Killing-Yano equations and G-structures
- Conformal supergravities as Chern-Simons theories revisited
- Some remarks on (super)-conformal Killing-Yano tensors
- Killing tensors and canonical geometry
- Notes on Super Killing Tensors
- Do Killing-Yano tensors form a Lie Algebra?
- Killing-Yano equations with torsion, worldline actions and G-structures
- Local metrics admitting a principal Killing-Yano tensor with torsion
- Integrability Conditions for Killing-Yano Tensors and Conformal Killing-Yano Tensors
- Super-Laplacians and their symmetries
- New currents with Killing-Yano tensors
- Symmetries of supergravity backgrounds in six dimensions
- Integrability Conditions for Killing-Yano Tensors and Maximally Symmetric Spaces in the Presence of Torsion
- Separation of variables in the WZW models