U-duality (sub-)groups and their topology

Details U-duality (sub-)groups and their topology U-duality (sub-)groups and their topology

2003-12-12

arxiv.org/abs/hep-th/0312134v1

Class.Quant.Grav. 21 (2004) S1367-1374

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 8 pages, 2 tables, 1 figure, uses IOP-style files. Contributed to the proceedings of the RTN-workshop ``The quantum str

Scientific paper

10.1088/0264-9381/21/10/009

We discuss some consequences of the fact that symmetry groups appearing in compactified (super-)gravity may be non-simply connected. The possibility to add fermions to a theory results in a simple criterion to decide whether a 3-dimensional coset sigma model can be interpreted as a dimensional reduction of a higher dimensional theory. Similar criteria exist for higher dimensional sigma models, though less decisive. Careful examination of the topology of symmetry groups rules out certain proposals for M-theory symmetries, which are not ruled out at the level of the algebra's. We conclude with an observation on the relation between the ``generalized holonomy'' proposal, and the actual symmetry groups resulting from E_10 and E_11 conjectures.

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