Non-compact symmetries, extended supergravities and the Wheeler-DeWitt equation

Nicolai, Hermann

doi:10.1016/0370-2693(90)91967-G

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Non-compact symmetries, extended supergravities and the Wheeler-DeWitt equation

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Nicolai, Hermann
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Nicolai, H. (1990). Non-compact symmetries, extended supergravities and the Wheeler-DeWitt equation. Physics Letters B, 235(3-4), 295-301. doi:10.1016/0370-2693(90)91967-G.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-5CF6-4

Abstract

The algebra of local and rigid symmetries of N=16 supergravity in three and two dimensions is considered. The conserved currents of the non-compact rigid E8 and E9 symmetries are explicitly given. On the physical states, the associated charges are found to commute with all local symmetries and, in particular, with the Wheeler-DeWitt hamiltonian. The solutions of the latter are therefore infinitely degenerate. This analysis sheds some new light on the significance of non-compact symmetries in extended supergravities. Furthermore, I argue that E9 plays the role of a “solution-generating group” for the Wheeler-DeWitt equation of N=16 supergravity in two dimensions, which should thus be completely integrable.