Poincare Duality and G+++ algebra's

Details Poincare Duality and G+++ algebra's Poincare Duality and G+++ algebra's

2005-10-24

arxiv.org/abs/hep-th/0510212v1

Commun.Math.Phys.275:491-527,2007

Physics

High Energy Physics

High Energy Physics - Theory

47 pages, 5 figures, LaTeX

Scientific paper

10.1007/s00220-007-0309-0

Theories with General Relativity as a sub-sector exhibit enhanced symmetries upon dimensional reduction, which is suggestive of ``exotic dualities''. Upon inclusion of time-like directions in the reductions one can dualize to theories in different space-time signatures. We clarify the nature of these dualities and show that they are well captured by the properties of infinite-dimensional symmetry algebra's (G+++ algebra's), but only after taking into account that the realization of Poincare duality leads to restrictions on the denominator subalgebra appearing in the non-linear realization. The correct realization of Poincare duality can be encoded in a simple algebraic constraint, that is invariant under the Weyl-group of the G+++ algebra, and therefore independent of the detailed realization of the theory under consideration. We also construct other Weyl-invariant quantities that can be used to extract information from the G+++ algebra without fixing a level decomposition.

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