Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-12-19
JHEP0402:033,2004
Physics
High Energy Physics
High Energy Physics - Theory
45 pages, 9 figures, 9 tables, tex
Scientific paper
10.1088/1126-6708/2004/02/033
We consider the decomposition of the adjoint and fundamental representations of very extended Kac-Moody algebras G+++ with respect to their regular A type subalgebra which, in the corresponding non-linear realisation, is associated with gravity. We find that for many very extended algebras almost all the A type representations that occur in the decomposition of the fundamental representations also occur in the adjoint representation of G+++. In particular, for E8+++, this applies to all its fundamental representations. However, there are some important examples, such as An+++, where this is not true and indeed the adjoint representation contains no generator that can be identified with a space-time translation. We comment on the significance of these results for how space-time can occur in the non-linear realisation based on G+++. Finally we show that there is a correspondence between the A representations that occur in the fundamental representation associated with the very extended node and the adjoint representation of G+++ which is consistent with the interpretation of the former as charges associated with brane solutions.
Kleinschmidt Axel
West Peter
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