Supergravity,the seven-sphere,and spontaneous symmetry breaking |
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Authors: | MJ Duff |
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Institution: | CERN, Geneva, Switzerland |
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Abstract: | N = 1 supergravity in d = 11 dimensions spontaneously compactifies on S7 to an N = 8 supergravity in d = 4 with a local SO(8) × SO(8) invariance, probably enlargeable to SO(8) × SU(8). Apart from group manifolds, S7 is the only compact manifold to admit an absolute parallelism. This permits (a) a “squashing” of S7 which gives expectation values to the scalar fields and (b) a parallelizing “torsion” which gives expectation values to the pseudoscalars. This correspondence between extrema of the d = 4 effective potential and solutions of the d = 11 field equations provides a Kaluza-Klein origin for the spontaneous breakdown of gauge symmetries, discrete symmetries, and supersymmetries. It also puts a new perspective on the puzzle of the cosmological constant. |
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