U-duality (sub-)groups and their topology

Abstract

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.

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 2003

References in corpus (9)

• E10 and a "small tension expansion" of M Theory
• $E_{11}$, SL(32) and Central Charges
• Locally supersymmetric D=3 non-linear sigma models
• Hidden Spacetime Symmetries and Generalized Holonomy in M-theory
• The group theory of oxidation
• The group theory of oxidation II: Cosets of non-split groups
• Integrability and Canonical Structure of d=2, N=16 Supergravity
• 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

Cited by in corpus (6)

• Generalised Geometry for M-Theory
• Extended E8 Invariance of 11-Dimensional Supergravity
• M-theory and E10: Billiards, Branes, and Imaginary Roots
• Poincare Duality and G+++ algebra's
• Time-like T-duality algebra
• Global aspects of moduli spaces of 2d SCFTs