From Topology to Generalised Dimensional Reduction

TL;DR

This paper broadens the scope of generalized dimensional reduction in supergravity theories by incorporating cohomology-based terms, leading to new massive supergravities with domain-wall solutions from higher-dimensional branes.

Contribution

It introduces a wider class of generalized reductions involving differential forms and cohomology, extending previous methods in supergravity compactifications.

Findings

Wider class of generalized reductions identified

Massive supergravities with domain-wall solutions constructed

Examples include reductions of M-theory and type II strings on complex manifolds

Abstract

In the usual procedure for toroidal Kaluza-Klein reduction, all the higher-dimensional fields are taken to be independent of the coordinates on the internal space. It has recently been observed that a generalisation of this procedure is possible, which gives rise to lower-dimensional ``massive'' supergravities. The generalised reduction involves allowing gauge potentials in the higher dimension to have an additional linear dependence on the toroidal coordinates. In this paper, we show that a much wider class of generalised reductions is possible, in which higher-dimensional potentials have additional terms involving differential forms on the internal manifold whose exterior derivatives yield representatives of certain of its cohomology classes. We consider various examples, including the generalised reduction of M-theory and type II strings on K3, Calabi-Yau and 7-dimensional Joyce manifolds. The resulting massive supergravities support domain-wall solutions that arise by the vertical dimensional reduction of higher-dimensional solitonic p-branes and intersecting p-branes.