N=8 Supergravity Breaks Down to N=1

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Supersymmetry

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The field equations of N=1 supergravity in d=11 dimensions admit a spontaneous compactification on the seven-sphere to an N=8 theory in d=4 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 S7 is distorted. The isometry group of this new solution is SO(5) ⊗ SU(2), the relevant holonomy group is G2, and the N=8 supersymmetry is broken down to N=1 at the Planck scale. The implications for grand unified theories are briefly discussed.

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