Higher-dimensional Origin of D=3 Coset Symmetries

TL;DR

This paper explores the origins of three-dimensional coset symmetries in supergravity theories, revealing a duality between rank and dimension and identifying the highest dimensions for their Kaluza-Klein origins.

Contribution

It generalizes the study of scalar sigma models G/H beyond supersymmetry, establishing their highest originating dimensions and uncovering a duality between rank and dimension.

Findings

Discovery of a duality between rank and dimension in coset models.

Identification of highest dimensions for Kaluza-Klein reduction of these models.

Analysis of Hermitean and quaternionic symmetric spaces.

Abstract

It is well known that the toroidal dimensional reduction of supergravities gives rise in three dimensions to theories whose bosonic sectors are described purely in terms of scalar degrees of freedom, which parameterise sigma-model coset spaces. For example, the reduction of eleven-dimensional supergravity gives rise to an E_8/SO(16) coset Lagrangian. In this paper, we dispense with the restrictions of supersymmetry, and study all the three-dimensional scalar sigma models G/H where G is a maximally-non-compact simple group, with H its maximal compact subgroup, and find the highest dimensions from which they can be obtained by Kaluza-Klein reduction. A magic triangle emerges with a duality between rank and dimension. Interesting also are the cases of Hermitean symmetric spaces and quaternionic spaces.