Spontaneous Supersymmetry Breaking by the Squashed Seven-Sphere

Abstract

Spontaneous compactification of $d=11$ supergravity on the squashed seven-sphere (${S}^{7}$) yields a spontaneously broken phase of the $N=8$ theory on the round ${S}^{7}$ with SO(8) broken to SO(5) \ensuremath{\bigotimes} SU(2) and with $N=1$ or $N=0$ supersymmetry according as the squashing is left or right handed. A feature unique to Kaluza-Klein supergravity is that the massless gravitino of the $N=1$ phase comes from a massive $N=8$ supermultiplet, as do the Higgs scalars. A solution is found with squashing and torsion but only in the right-squashed ($N=0$) case.