TCFHs, hidden symmetries and M-theory backgrounds
arXiv:2201.11563 · doi:10.1088/1361-6382/aca1a2
Abstract
We present the TCFH of 11-dimensional supergravity and so demonstrate that the form bilinears of supersymmetric solutions satisfy a generalisation of the conformal Killing-Yano equation with resepct to the TCFH connection. We also compute the Killing-Stäckel, Killing-Yano and closed conformal Killing-Yano tensors of all spherically symmetric M-branes that include the M2-brane, M5-brane, KK-monopole and pp-wave and demonstrate that their geodesic flows are completely integrable by giving all independent conserved charges in involution. We then find that all form bilinears of pp-wave and KK-monopole solutions generate (hidden) symmetries for spinning particle probes propagating on these backgrounds. Moreover, there are Killing spinors such that some of the 1-, 2- and 3-form bilinears of the M2-brane solution also generate symmetries for spinning particle probes. We also explore the question on whether the form bilinears are sufficient to prove the integrability of particle probe dynamics on 11-dimensional supersymmetric backgrounds.
arXiv comment27 pages
References in corpus (31)
- Unity of Superstring Dualities
- D-branes from M-branes
- The Geometry of D=11 Killing Spinors
- SUSY in the sky
- Black holes, hidden symmetries, and complete integrability
- HKT and OKT Geometries on Soliton Black Hole Moduli Spaces
- Maximally supersymmetric solutions of ten- and eleven-dimensional supergravities
- The Geometry of D=11 Null Killing Spinors
- Killing-Yano Tensors, Rank-2 Killing Tensors, and Conserved Quantities in Higher Dimensions
- Hidden Symmetries of Dynamics in Classical and Quantum Physics
- Hidden Spacetime Symmetries and Generalized Holonomy in M-theory
- Holonomy and Symmetry in M-theory
- Holonomy groups and W-symmetries
- Generalized hidden symmetries and the Kerr-Sen black hole
- Conserved gravitational charges from Yano tensors
- Killing(-Yano) Tensors in String Theory
- Symmetries of the Dirac operator with skew-symmetric torsion
- Killing-Yano tensors and some applications
- Killing-Yano Supersymmetry in String Theory
- Killing-Yano equations and G-structures
- Classification, geometry and applications of supersymmetric backgrounds
- Generalized Taub-NUT metrics and Killing-Yano tensors
- Some remarks on (super)-conformal Killing-Yano tensors
- The holonomy of the supercovariant connection and Killing spinors
- Killing-Yano equations with torsion, worldline actions and G-structures
- Killing tensors in pp-wave spacetimes
- Twisted form hierarchies, Killing-Yano equations and supersymmetric backgrounds
- Symmetries, Spinning Particles and the TCFH of D=4,5 Minimal Supergravities
- TCFHs, hidden symmetries and type II theories
- Killing-Yano symmetry for a class of spacetimes admitting parallel null 1-planes
- Choices of spinor inner products on M-theory backgrounds