### Abstract

We study quantum gravity in 2 + ε{lunate} dimensions in such a way as to preserve the volume-preserving diffeomorphism invariance. In such a formulation, we prove the following trinity: the general covariance, the conformal invariance and the renormalization group flow to the Einstein theory at long distance. We emphasize that the consistent and macroscopic universes like our own can only exist for a matter central charge 0 < c < 25. We show that the spacetime singularity at the big bang is resolved by the renormalization effect and universes are found to bounce back from the big crunch. Our formulation may be viewed as a Ginzburg-Landau theory which can describe both the broken and the unbroken phase of quantum gravity and the phase transition between them.

Original language | English |
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Pages (from-to) | 158-180 |

Number of pages | 23 |

Journal | Nuclear Physics, Section B |

Volume | 427 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Sep 26 1994 |

Externally published | Yes |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

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## Cite this

*Nuclear Physics, Section B*,

*427*(1-2), 158-180. https://doi.org/10.1016/0550-3213(94)90273-9