### Abstract

We study two-loop renormalization in (2 + ε{lunate})-dimensional quantum gravity. As a first step towards the full calculation, we concentrate on the divergences which are proportional to the number of matter fields. We calculate the β functions and show how the nonlocal divergences as well as the infrared divergences cancel among the diagrams. Although the formalism includes a subtlety concerning the general covariance due to the dynamics of the conformal mode, we find that the renormalization group allows the existence of a fixed point which possesses the general covariance. Our results strongly suggest that we can construct a consistent theory of quantum gravity by the ε{lunate} expansion around two dimensions.

Original language | English |
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Pages (from-to) | 353-380 |

Number of pages | 28 |

Journal | Nuclear Physics, Section B |

Volume | 444 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Jun 19 1995 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics, Section B*,

*444*(1-2), 353-380. https://doi.org/10.1016/0550-3213(95)00071-Y