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Journal Article

On KE(9)


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

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Nicolai, H., & Samtleben, H. (2005). On KE(9). Quarterly Journal of Pure and Applied Mathematics, 1, 180-204.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-4E5A-2
We study the maximal compact subgroup K(E_9) of the affine Lie group E_9(9) and its on-shell realization as an R symmetry of maximal N=16 supergravity in two dimensions. We first give a rigorous definition of the group K(E_9), which lives on the double cover of the spectral parameter plane, and show that the infinitesimal action of K(E_9) on the chiral components of the bosons and the fermions is determined in terms of an expansion of the Lie algebra of K(E_9) about the two branch points of this cover; this implies in particular that the fermions of N=16 supergravity transform in a spinor representation of K(E_9). The fermionic equations of motion can be fitted into the lowest components of a single K(E_9) covariant `Dirac equation', with the linear system of N=16 supergravity as the gauge connection. These results suggest the existence of an `off-shell' realization of K(E_9) in terms of an infinite component spinor representation. We conclude with some coments on `generalized holonomies' of M theory.