### Abstract

I review some of the salient points of the construction of a perturbative quantum theory of the dimensionally reduced pure Einstein gravity from 4 to 2 dimensions assuming that the 4 dimensional (4D) metrics admit two commuting Killing vectors. The dimensionally reduced theory corresponds to an 0(1,2) symmetric σ-model coupled to two scalar fields in flat spacetime. It inherits the lack of standard perturbative renormalizability from 4D gravity, however, it turns out that strict cutoff independence can be achieved to all loop orders in a space of Lagrangians differing only by a field dependent conformai factor. The renormalization group flow possesses a unique non-Gaussian fixed point at which the trace anomaly vanishes. The existence of this non-Gaussian fixed point is compatible with Weinberg's "asymptotic safety" scenario.

Original language | English |
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Title of host publication | Gribov Memorial Volume |

Subtitle of host publication | Quarks, Hadrons, and Strong Interactions - Proceedings of the Memorial Workshop Devoted to the 75th Birthday of V N Gribov |

Publisher | World Scientific Publishing Co. Pte Ltd |

Pages | 522-535 |

Number of pages | 14 |

ISBN (Print) | 9812567569, 9789812567567 |

DOIs | |

Publication status | Published - 2006 |

Event | Gribov Memorial Workshop Devoted to the 75th Birthday of V N Gribov: Quarks, Hadrons, and Strong Interactions - Budapest, Hungary Duration: May 22 2005 → May 24 2005 |

### Publication series

Name | Gribov Memorial Volume: Quarks, Hadrons, and Strong Interactions - Proceedings of the Memorial Workshop Devoted to the 75th Birthday of V N Gribov |
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### Other

Other | Gribov Memorial Workshop Devoted to the 75th Birthday of V N Gribov: Quarks, Hadrons, and Strong Interactions |
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Country | Hungary |

City | Budapest |

Period | 5/22/05 → 5/24/05 |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

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## Cite this

*Gribov Memorial Volume: Quarks, Hadrons, and Strong Interactions - Proceedings of the Memorial Workshop Devoted to the 75th Birthday of V N Gribov*(pp. 522-535). (Gribov Memorial Volume: Quarks, Hadrons, and Strong Interactions - Proceedings of the Memorial Workshop Devoted to the 75th Birthday of V N Gribov). World Scientific Publishing Co. Pte Ltd. https://doi.org/10.1142/9789812773784_0045