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High Energy Physics - Theory, hep-th
Abstract:
We consider the relation between higher spin gauge fields and real Kac-Moody
Lie algebras. These algebras are obtained by double and triple extensions of
real forms g_0 of the finite-dimensional simple algebras g arising in
dimensional reductions of gravity and supergravity theories. Besides providing
an exhaustive list of all such algebras, together with their associated
involutions and restricted root diagrams, we are able to prove general
properties of their spectrum of generators w.r.t. a decomposition of the triple
extension of g_0 under its gravity subalgebra gl(D,R). These results are then
combined with known consistent models of higher spin gauge theory to prove that
all but finitely many generators correspond to non-propagating fields and there
are no higher spin fields contained in the Kac-Moody algebra.
