The topology of U-duality (sub)groups

Abstract

We discuss the topology of the symmetry groups appearing in compactified\n(super-)gravity, and discuss two applications. First, we demonstrate that for 3\ndimensional sigma models on a symmetric space G/H with G non-compact and H the\nmaximal compact subgroup of G, the possibility of oxidation to a higher\ndimensional theory can immediately be deduced from the topology of H. Second,\nby comparing the actual symmetry groups appearing in maximal supergravities\nwith the subgroups of SL(32,R) and Spin(32), we argue that these groups cannot\nserve as a local symmetry group for M-theory in a formulation of de Wit-Nicolai\ntype.\n