Research output: Contribution to journal › Article

Journal | Nuclear Physics B |
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Date | Published - 30 Jul 1990 |

Issue number | 2 |

Volume | 339 |

Number of pages | 25 |

Pages (from-to) | 491-515 |

Original language | English |

We examine the question of whether fundamental fermions can be regarded as topological solitons (geons) of a theory of pure quantum gravity in n + 4 dimensions. In particular, we consider the quantum gravitational field for (n + 4)-dimensional space-times which have asymptotic Kaluza-Klein behavior: asymptotic topology of the form R^{4} × G/H and a metric that is asymptotically the direct sum of the Minkowski metric on R^{4} and the natural symmetric metric on G/H. We argue that if there is a nonsingular theory of pure quantum gravity (a theory that, below Planck energy, involves only the space-time metric), then there are stable ground states with the kinematical quantum numbers of fundamental fermions: that is, states which have spin 1 2 and belong to the fundamental representation of G. Multi-valued representations of the asymptotic symmetry group can arise from diffeomorphisms (diffeos) of the (n + 3)-dimensional space that are not isotopic to the identity. In a path integral approach, the creation of fundamental fermions (topological geons) requires a space-time in which the topology of space-like hypersurfaces changes and in which the relevant diffeos on the final (n + 3)-space (containing the geons) are not extendible to diffeos of the (n + 4)-space-time. We prove that such pair-creation geometries occur in a lorentzian as well as euclidean framework and that the diffeos are not extendible. Although zero-mass modes of finite-size fermions need not belong to a real representation of the internal group, it is not difficult to prove that, independent of the fermion size, one cannot avoid mirror fermions. There is, however, an interesting loophole: A nonzero vacuum expectation value of a Higgs-like vector constructed from the metric can break chiral invariance without changing the lowest-order Einstein-Yang-Mills form of the gravitational lagrangian.

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