Domain Walls from M-branes

TL;DR

This paper explores how M-branes can be dimensionally reduced to domain walls in lower dimensions, requiring a generalized Kaluza-Klein ansatz for 7D but not for 4D, with implications for M-theory compactifications.

Contribution

It introduces a generalized Kaluza-Klein approach for reducing M-branes to domain walls in D=7, extending previous methods, and clarifies conditions for D=4 reductions without such generalization.

Findings

Generalized ansatz needed for D=7 reduction

No generalization needed for D=4 reduction

Extended previous toroidal compactification results

Abstract

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.