Domain Walls in Massive Supergravities

TL;DR

This paper shows that toroidally compactified D=11 supergravity can be consistently truncated to yield a family of maximally supersymmetric massive supergravities in D≤8 through Scherk–Schwarz reductions that assign linear z-dependence to axions. The key mechanism generates both mass terms for several form fields and cosmological-type terms, with the resulting theories forming a rich zoo of inequivalent models due to non-commutativity with U-duality and ordinary Kaluza–Klein reductions. The authors explicitly construct and catalog multiple D=8 and D=7 cases, analyze their residual symmetries, and demonstrate that these massive theories admit (D−2)-brane domain-wall solutions preserving half the supersymmetry, which can be oxidized back to D=11 (and in some cases to D=10) to yield new higher-dimensional solutions. They further generalize to reductions on multiple axions, yielding multi-parameter massive theories and multi-scalar domain walls, and discuss the higher-dimensional interpretation and limitations, including the special role of Δ=4/N domain walls and the non-universality of the massive theories arising from different reduction paths.

Abstract

We show how toroidally-compactified eleven-dimensional supergravity can be consistently truncated to yield a variety of maximally-supersymmetric ``massive'' supergravities in spacetime dimensions $D\le 8$. The mass terms arise as a consequence of making a more general ansatz than that in usual Kaluza-Klein dimensional reduction, in which one or more axions are given an additional linear dependence on one of the compactification coordinates. The lower-dimensional theories are nevertheless consistent truncations of eleven-dimensional supergravity. Owing to the fact that the generalised reduction commutes neither with U-duality nor with ordinary dimensional reduction, many different massive theories can result. The simplest examples arise when just a single axion has the additional linear coordinate dependence. We find five inequivalent such theories in D=7, and 71 inequivalent ones in D=4. The massive theories admit no maximally-symmetric vacuum solution, but they do admit $(D-2)$-brane solutions, i.e. domain walls, which preserve half the supersymmetry. We present examples of these solutions, and their oxidations to D=11. Some of the latter are new solutions of D=11 supergravity.