English

Representations of G+++ and the role of space-time

High Energy Physics - Theory 2009-11-10 v1

Abstract

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.

Keywords

Cite

@article{arxiv.hep-th/0312247,
  title  = {Representations of G+++ and the role of space-time},
  author = {A. Kleinschmidt and P. West},
  journal= {arXiv preprint arXiv:hep-th/0312247},
  year   = {2009}
}

Comments

45 pages, 9 figures, 9 tables, tex