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キーワード:
High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc
要旨:
A coset model based on the hyperbolic Kac-Moody algebra E10 has been
conjectured to underly eleven-dimensional supergravity and M theory. In this
note we study the canonical structure of the bosonic model for finite- and
infinite-dimensional groups. In the case of finite-dimensional groups like
GL(n) we exhibit a convenient set of variables with Borel-type canonical
brackets. The generalisation to the Kac-Moody case requires a proper treatment
of the imaginary roots that remains elusive. As a second result, we show that
the supersymmetry constraint of D=11 supergravity can be rewritten in a
suggestive way using E10 algebra data. Combined with the canonical structure,
this rewriting explains the previously observed association of the canonical
constraints with null roots of E10. We also exhibit a basic incompatibility
between local supersymmetry and the K(E10) `R symmetry', that can be traced
back to the presence of imaginary roots and to the unfaithfulness of the spinor
representations occurring in the present formulation of the E10 worldline
model, and that may require a novel type of bosonisation/fermionisation for its
resolution. This appears to be a key challenge for future progress with E10.
