• Corpus ID: 119459271

On K(E_9)

@article{Nicolai2004OnK,
  title={On K(E\_9)},
  author={Hermann Nicolai and H. Samtleben},
  journal={arXiv: High Energy Physics - Theory},
  year={2004}
}

• H. Nicolai, H. Samtleben
• Published 8 July 2004
• Mathematics, Physics
• arXiv: High Energy Physics - Theory

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.