### Abstract

Abstract: The explicit expressions for the one-loop non-perturbative corrections to the gravitational effective action induced by a scalar field on a stationary gravitational background are obtained both at zero and finite temperatures. The perturbative and non-perturbative contributions to the one-loop effective action are explicitly separated. It is proved that, after a suitable renormalization, the perturbative part of the effective action at zero temperature can be expressed in a covariant form solely in terms of the metric and its derivatives. This part coincides with the known large mass expansion of the one-loop effective action. The non-perturbative part of the renormalized one-loop effective action at zero temperature is proved to depend explicitly on the Killing vector defining the vacuum state of quantum fields. This part cannot be expressed in a covariant way through the metric and its derivatives alone. The implications of this result for the structure and symmetries of the effective action for gravity are discussed.

Original language | English |
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Article number | 111 |

Journal | Journal of High Energy Physics |

Volume | 2014 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2014 |

Externally published | Yes |

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### Keywords

- Anomalies in Field and String Theories
- Models of Quantum Gravity
- Nonperturbative Effects
- Renormalization Regularization and Renormalons

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2014*(8), [111]. https://doi.org/10.1007/JHEP08(2014)111