The field equations of $N=1\mathrm{}$ supergravity in $d=11\mathrm{}$ dimensions admit a spontaneous compactification on the seven-sphere to an $N=8\mathrm{}$ theory in $d=4\mathrm{}$ with local SO(8) invariance. A spontaneously broken version of this theory is provided by another solution of the field equations for which the metric on $S^7$ is distorted. The isometry group of this new solution is SO(5) ⊗ SU(2), the relevant holonomy group is $G_2$, and the $N=8\mathrm{}$ supersymmetry is broken down to $N=1\mathrm{}$ at the Planck scale. The implications for grand unified theories are briefly discussed.

• Received 9 December 1982

DOI:https://doi.org/10.1103/PhysRevLett.50.294