Kaluza-Klein Supergravity 2025

TL;DR

This paper revisits 1980s work on eleven-dimensional supergravity compactified on different S^7 geometries, exploring their implications for supersymmetry, stability, and consistent truncations in four dimensions.

Contribution

It provides a comprehensive review of Kaluza-Klein compactifications of maximal supergravity on S^7, emphasizing their broader applications and historical significance.

Findings

Different S^7 compactifications yield various supersymmetry levels.

The work highlights the role of squashing and Higgs mechanisms in supergravity.

Applications include vacuum stability and consistent truncations.

Abstract

We recall our work in the 1980s taking seriously the maximal eleven dimensions of supergravity, in particular the round, left squashed and right squashed $S^7$ compactifications to $D=4$ yielding $\mathcal N=8$, $\mathcal N=1$ and $\mathcal N=0$, respectively. This involved Kaluza-Kein techniques that have found wider applications such as spontaneous compactification, holonomy and supersymmetry, topology versus geometry, squashing and Higgs, vacuum stability and consistent truncations.