From Topology to Generalised Dimensional Reduction

TL;DR

This paper shows that relaxing the standard Kaluza–Klein ansatz to allow higher-dimensional gauge potentials to include cohomology-representative terms yields a broad class of consistent, lower-dimensional massive supergravities with domain-wall vacua. By applying cohomology-based generalized reductions to Type IIA, M-theory, and Type IIB on $T^4$, $K3$, $T^6$, Calabi–Yau, and Joyce manifolds, the authors derive domain-wall solutions that descend from vertical reductions of higher-dimensional solitons and intersecting branes. The work reveals both the richness of possible massive theories and the intricate effects on dualities, showing that some dual relationships survive only in specific generalized settings (e.g., IIA on K3 vs M-theory on K3×$S^1$). Notably, reductions on Joyce manifolds yield multi-brane interplays (e.g., seven intersecting 5-branes) and connect to four-dimensional $N=1$ massive supergravity with domain-wall vacua. Overall, the results provide a cohesive framework linking internal topology, massive supergravities, and brane physics across M-theory and Type II theories.

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.