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

Pages | 522-535 |

Number of pages | 14 |

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 |

### 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 |

### Fingerprint

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### 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)

**Quantum Einstein gravity and asymptotic safety.** / Forgács, P.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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 Workshop Devoted to the 75th Birthday of V N Gribov: Quarks, Hadrons, and Strong Interactions, Budapest, Hungary, 5/22/05.

}

TY - GEN

T1 - Quantum Einstein gravity and asymptotic safety

AU - Forgács, P.

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84894480623&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84894480623&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84894480623

SN - 9812567569

SN - 9789812567567

SP - 522

EP - 535

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

ER -