Kaluza-Klein Supergravity 2025

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.