Domain Walls from M-branes

We discuss the vertical dimensional reduction of M-branes to domain walls in D = 7 and D = 4, by dimensional reduction on Ricci-flat 4-manifolds and 7-manifolds. In order to interpret the vertically-reduced 5-brane as a domain wall solution of a dimensionally-reduced theory in D = 7, it is necessary to generalise the usual Kaluza-Klein ansatz, so that the 3-form potential in D = 11 has an additional term that can generate the necessary cosmological term in D = 7. We show how this can be done for general 4-manifolds, extending previous results for toroidal compactifications. By contrast, no generalisation of the Kaluza-Klein ansatz is necessary for the compactification of M-theory to a D = 4 theory that admits the domain wall solution coming from the membrane in D = 11.