TCFHs, hidden symmetries and M-theory backgrounds

G. Papadopoulos*, E. Pérez-Bolaños

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
35 Downloads (Pure)


We present the twisted covariant form hierarchy (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, KY 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 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.

Original languageEnglish
Article number245015
JournalClassical and Quantum Gravity
Issue number24
Publication statusPublished - 25 Nov 2022


  • hidden symmetries
  • Killing spinor equations
  • Killing-Yano tensors
  • M-branes
  • TCFHs


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