TCFHs, hidden symmetries and M-theory backgrounds

TY - JOUR

T1 - TCFHs, hidden symmetries and M-theory backgrounds

AU - Papadopoulos, G.

AU - Pérez-Bolaños, E.

N1 - Funding Information: EPB is supported by the CONACYT, the Mexican Council of Science. Publisher Copyright: © 2022 The Author(s). Published by IOP Publishing Ltd.

PY - 2022/11/25

Y1 - 2022/11/25

N2 - 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.

AB - 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.

KW - hidden symmetries

KW - Killing spinor equations

KW - Killing-Yano tensors

KW - M-branes

KW - TCFHs

UR - http://www.scopus.com/inward/record.url?scp=85143613894&partnerID=8YFLogxK

U2 - 10.1088/1361-6382/aca1a2

DO - 10.1088/1361-6382/aca1a2

M3 - Article

AN - SCOPUS:85143613894

SN - 0264-9381

VL - 39

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

IS - 24

M1 - 245015

ER -