The topology of U-duality (sub-)groups

TL;DR

This paper explores the topology of symmetry groups in compactified supergravity theories, showing how topological properties influence the possibility of oxidation and constraining candidate symmetry groups for M-theory.

Contribution

It provides a topological analysis of symmetry groups in supergravity, linking group topology to physical properties like oxidation and M-theory symmetry constraints.

Findings

Topology of H determines oxidation possibilities.

Symmetry groups in supergravity cannot be subgroups of SL(32,R) or Spin(32).

Constraints on M-theory symmetry formulations.

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.