5 research outputs found
U-duality (sub-)groups and their topology
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.Comment: LaTeX, 8 pages, 2 tables, 1 figure, uses IOP-style files. Contributed
to the proceedings of the RTN-workshop ``The quantum structure of space-time
and the geometrical nature of the fundamental interactions,'', Copenhagen,
Denmark, september 200
The topology of U-duality (sub-)groups
We discuss the topology of the symmetry groups appearing in compactified
(super-)gravity, and discuss two applications. First, we demonstrate that for 3
dimensional sigma models on a symmetric space G/H with G non-compact and H the
maximal compact subgroup of G, the possibility of oxidation to a higher
dimensional theory can immediately be deduced from the topology of H. Second,
by comparing the actual symmetry groups appearing in maximal supergravities
with the subgroups of SL(32,R) and Spin(32), we argue that these groups cannot
serve as a local symmetry group for M-theory in a formulation of de Wit-Nicolai
type.Comment: 18 pages, LaTeX, 1 figure, 2 table