TCFHs, hidden symmetries and type II theories
arXiv:2111.15405 · doi:10.1007/JHEP07(2022)097
Abstract
We present the twisted covariant form hierarchies (TCFH) of type IIA and IIB 10-dimensional supergravities and show that all form bilinears of supersymmetric backgrounds satisfy the conformal Killing-Yano equation with respect to a TCFH connection. We also compute the Killing-Stäckel, Killing-Yano and closed conformal Killing-Yano tensors of all spherically symmetric type II brane backgrounds and demonstrate that the geodesic flow on these solutions is completely integrable by giving all independent charges in involution. We then identify all form bilinears of common sector and D-brane backgrounds which generate hidden symmetries for particle and string probe actions. We also explore the question on whether charges constructed from form bilinears are sufficient to prove the integrability of probes on supersymmetric backgrounds.
68 pages
References in corpus (9)
- Hidden Symmetries of Dynamics in Classical and Quantum Physics
- Holonomy and Symmetry in M-theory
- Geometry of all supersymmetric type I backgrounds
- IIA Ten-forms and the Gauge Algebras of Maximal Supergravity Theories
- Generalized hidden symmetries and the Kerr-Sen black hole
- Symmetries of the Dirac operator with skew-symmetric torsion
- Killing-Yano equations and G-structures
- Covariantly constant forms on torsionful geometries from world-sheet and spacetime perspectives
- Symmetries, Spinning Particles and the TCFH of D=4,5 Minimal Supergravities