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On K(E_9) | H. Nicolai
; H. Samtleben
; | Date: |
8 Jul 2004 | Journal: | Q.J.Pure Appl.Math. 1 (2005) 180-204 | Subject: | hep-th | Abstract: | 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. | Source: | arXiv, hep-th/0407055 | Services: | Forum | Review | PDF | Favorites |
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