Fibre Bundles and Generalised Dimensional Reduction

TL;DR

This paper explores the geometrical and topological properties of generalized dimensional reductions in supergravity theories, revealing how global symmetries influence the structure and consistency of lower-dimensional massive theories.

Contribution

It provides a detailed analysis of the topological restrictions and structures arising from generalized reductions of supergravities in D=11 and D=10 dimensions.

Findings

Topological restrictions on compactification parameters

Structure of internal spaces in generalized reductions

Examples include reductions of type IIA and IIB supergravity

Abstract

We study some geometrical and topological aspects of the generalised dimensional reduction of supergravities in D=11 and D=10 dimensions, which give rise to massive theories in lower dimensions. In these reductions, a global symmetry is used in order to allow some of the fields to have a non-trivial dependence on the compactifying coordinates. Global consistency in the internal space imposes topological restrictions on the parameters of the compactification as well as the structure of the space itself. Examples that we consider include the generalised reduction of the type IIA and type IIB theories on a circle, and also the massive ten-dimensional theory obtained by the generalised reduction of D=11 supergravity.