Bare action and regularized functional integral of asymptotically safe quantum gravity
Abstract
Investigations of quantum Einstein gravity (QEG) based upon the effective average action employ a flow equation which does not contain any ultraviolet (UV) regulator. Its renormalization group trajectories emanating from a nonGaussian fixed point define asymptotically safe quantum field theories. A priori these theories are, somewhat unusually, given in terms of their effective rather than bare action. In this paper we construct a functional integral representation of these theories. We fix a regularized measure and show that every trajectory of effective average actions, depending on an IR cutoff only, induces an associated trajectory of bare actions which depend on a UV cutoff. Together with the regularized measure these bare actions give rise to a functional integral which reproduces the prescribed effective action when the UV cutoff is removed. In this way we are able to reconstruct the underlying microscopic (classical) system and identify its fundamental degrees of freedom and interactions. The bare action of the EinsteinHilbert truncation is computed and its flow is analyzed as an example. Various conceptual issues related to the completion of the asymptotic safety program are discussed.
 Authors:

 Institute of Physics, University of Mainz, Staudingerweg 7, D55099 Mainz (Germany)
 Publication Date:
 OSTI Identifier:
 21259834
 Resource Type:
 Journal Article
 Journal Name:
 Physical Review. D, Particles Fields
 Additional Journal Information:
 Journal Volume: 79; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.79.025008; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 05562821
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ASYMPTOTIC SOLUTIONS; DEGREES OF FREEDOM; EQUATIONS; GENERAL RELATIVITY THEORY; GRAVITATION; INTERACTIONS; QUANTUM FIELD THEORY; QUANTUM GRAVITY; RENORMALIZATION; TRAJECTORIES; ULTRAVIOLET RADIATION
Citation Formats
Manrique, Elisa, and Reuter, Martin. Bare action and regularized functional integral of asymptotically safe quantum gravity. United States: N. p., 2009.
Web. doi:10.1103/PHYSREVD.79.025008.
Manrique, Elisa, & Reuter, Martin. Bare action and regularized functional integral of asymptotically safe quantum gravity. United States. https://doi.org/10.1103/PHYSREVD.79.025008
Manrique, Elisa, and Reuter, Martin. Thu .
"Bare action and regularized functional integral of asymptotically safe quantum gravity". United States. https://doi.org/10.1103/PHYSREVD.79.025008.
@article{osti_21259834,
title = {Bare action and regularized functional integral of asymptotically safe quantum gravity},
author = {Manrique, Elisa and Reuter, Martin},
abstractNote = {Investigations of quantum Einstein gravity (QEG) based upon the effective average action employ a flow equation which does not contain any ultraviolet (UV) regulator. Its renormalization group trajectories emanating from a nonGaussian fixed point define asymptotically safe quantum field theories. A priori these theories are, somewhat unusually, given in terms of their effective rather than bare action. In this paper we construct a functional integral representation of these theories. We fix a regularized measure and show that every trajectory of effective average actions, depending on an IR cutoff only, induces an associated trajectory of bare actions which depend on a UV cutoff. Together with the regularized measure these bare actions give rise to a functional integral which reproduces the prescribed effective action when the UV cutoff is removed. In this way we are able to reconstruct the underlying microscopic (classical) system and identify its fundamental degrees of freedom and interactions. The bare action of the EinsteinHilbert truncation is computed and its flow is analyzed as an example. Various conceptual issues related to the completion of the asymptotic safety program are discussed.},
doi = {10.1103/PHYSREVD.79.025008},
url = {https://www.osti.gov/biblio/21259834},
journal = {Physical Review. D, Particles Fields},
issn = {05562821},
number = 2,
volume = 79,
place = {United States},
year = {2009},
month = {1}
}