The topology of U-duality (sub-)groups

Abstract

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.

18 pages, LaTeX, 1 figure, 2 tables

References in corpus (22)

• E_11 and M Theory
• E10 and a "small tension expansion" of M Theory
• Dualisation of Dualities, I
• $E_{11}$, SL(32) and Central Charges
• E_(10), BE_(10) and Arithmetical Chaos in Superstring Cosmology
• Kac-Moody Symmetries of IIB Supergravity
• Higher-dimensional Origin of D=3 Coset Symmetries
• Hidden Spacetime Symmetries and Generalized Holonomy in M-theory
• Holonomy and Symmetry in M-theory
• Duality and Moduli Spaces for Time-Like Reductions
• Borcherds symmetries in M-theory
• The group theory of oxidation
• The group theory of oxidation II: Cosets of non-split groups
• The holonomy of IIB supercovariant connection
• Brane Rotating Symmetries and the Fivebrane Equations of Motion
• Real Borcherds Superalgebras and M-theory
• Non-trivial flat connections on the 3-torus I: G_2 and the orthogonal groups
• Non-trivial flat connections on the 3-torus II: The exceptional groups F_4 and E_6,7,8
• The holonomy of the supercovariant connection and Killing spinors
• Low Level Representations for E10 and E11
• Oxidation = group theory
• Symmetries in M-theory: Monsters, Inc

Cited by in corpus (16)

• Generalised Geometry for M-Theory
• Hidden symmetries and the fermionic sector of eleven-dimensional supergravity
• E_11: Sign of the times
• Extended E8 Invariance of 11-Dimensional Supergravity
• K(E10), Supergravity and Fermions
• M-theory and E10: Billiards, Branes, and Imaginary Roots
• Hidden Symmetries and Dirac Fermions
• K(E9) from K(E10)
• Generalized holonomy of M-theory vacua
• E(7(7)) and d=11 supergravity
• Poincare Duality and G+++ algebra's
• Kac-Moody Algebras in M-theory
• Killing Spinor Equations from Nonlinear Realisations
• Erice lectures on "The status of local supersymmetry"
• Generalised holonomies and K(E${}_9$)
• Unifying R-symmetry in M-theory