FROM TOPOLOGY TO GENERALIZED DIMENSIONAL REDUCTION

In the usual procedure for toroidal Kaluza-Klein reduction, all the hi gher-dimensional fields are taken to be independent of the coordinates on the internal space. It has recently been observed that a generalis ation of this procedure is possible, which gives rise to lower-dimensi onal massive supergravities. The generalised reduction involves allowi ng gauge potentials in the higher dimension to have an additional line ar dependence on the toroidal coordinates. In this paper, we show that a much wider class of generalised reductions is possible, in which hi gher-dimensional potentials have additional terms involving differenti al forms on the internal manifold whose exterior derivatives yield rep resentatives 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 resu lting massive supergravities support domain-wall solutions that arise by the vertical dimensional reduction of higher-dimensional solitonic p-branes and intersecting p-branes. (C) 1997 Published by Elsevier Sci ence B.V.