### 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 |
---|---|

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

**Two-loop renormalization in quantum gravity near two dimensions.** / Aida, Toshiaki; Kitazawa, Yoshihisa; Nishimura, Jun; Tsuchiya, Asato.

Research output: Contribution to journal › Article

*Nuclear Physics, Section B*, vol. 444, no. 1-2, pp. 353-380. https://doi.org/10.1016/0550-3213(95)00071-Y

}

TY - JOUR

T1 - Two-loop renormalization in quantum gravity near two dimensions

AU - Aida, Toshiaki

AU - Kitazawa, Yoshihisa

AU - Nishimura, Jun

AU - Tsuchiya, Asato

PY - 1995/6/19

Y1 - 1995/6/19

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0000593103&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000593103&partnerID=8YFLogxK

U2 - 10.1016/0550-3213(95)00071-Y

DO - 10.1016/0550-3213(95)00071-Y

M3 - Article

AN - SCOPUS:0000593103

VL - 444

SP - 353

EP - 380

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 1-2

ER -