Background independence and asymptotic safety in conformally reduced gravity
Abstract
We analyze the conceptual role of background independence in the application of the effective average action to quantum gravity. Insisting on a background independent renormalization group (RG) flow the coarse graining operation must be defined in terms of an unspecified variable metric since no rigid metric of a fixed background spacetime is available. This leads to an extra field dependence in the functional RG equation and a significantly different RG flow in comparison to the standard flow equation with a rigid metric in the mode cutoff. The background independent RG flow can possess a nonGaussian fixed point, for instance, even though the corresponding standard one does not. We demonstrate the importance of this universal, essentially kinematical effect by computing the RG flow of quantum Einstein gravity in the 'conformally reduced' EinsteinHilbert approximation which discards all degrees of freedom contained in the metric except the conformal one. Without the extra field dependence the resulting RG flow is that of a simple {phi}{sup 4} theory. By including it one obtains a flow with exactly the same qualitative properties as in the full EinsteinHilbert truncation. In particular it possesses the nonGaussian fixed point which is necessary for asymptotic safety.
 Authors:

 Institute of Physics, University of Mainz, Staudingerweg 7, D55099 Mainz (Germany)
 Publication Date:
 OSTI Identifier:
 21296368
 Resource Type:
 Journal Article
 Journal Name:
 Physical Review. D, Particles Fields
 Additional Journal Information:
 Journal Volume: 79; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.79.105005; (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; APPROXIMATIONS; ASYMPTOTIC SOLUTIONS; COMPARATIVE EVALUATIONS; DEGREES OF FREEDOM; EQUATIONS; GRAVITATION; METRICS; QUANTUM GRAVITY; RENORMALIZATION; SPACETIME
Citation Formats
Reuter, M, and Weyer, H. Background independence and asymptotic safety in conformally reduced gravity. United States: N. p., 2009.
Web. doi:10.1103/PHYSREVD.79.105005.
Reuter, M, & Weyer, H. Background independence and asymptotic safety in conformally reduced gravity. United States. https://doi.org/10.1103/PHYSREVD.79.105005
Reuter, M, and Weyer, H. Fri .
"Background independence and asymptotic safety in conformally reduced gravity". United States. https://doi.org/10.1103/PHYSREVD.79.105005.
@article{osti_21296368,
title = {Background independence and asymptotic safety in conformally reduced gravity},
author = {Reuter, M and Weyer, H},
abstractNote = {We analyze the conceptual role of background independence in the application of the effective average action to quantum gravity. Insisting on a background independent renormalization group (RG) flow the coarse graining operation must be defined in terms of an unspecified variable metric since no rigid metric of a fixed background spacetime is available. This leads to an extra field dependence in the functional RG equation and a significantly different RG flow in comparison to the standard flow equation with a rigid metric in the mode cutoff. The background independent RG flow can possess a nonGaussian fixed point, for instance, even though the corresponding standard one does not. We demonstrate the importance of this universal, essentially kinematical effect by computing the RG flow of quantum Einstein gravity in the 'conformally reduced' EinsteinHilbert approximation which discards all degrees of freedom contained in the metric except the conformal one. Without the extra field dependence the resulting RG flow is that of a simple {phi}{sup 4} theory. By including it one obtains a flow with exactly the same qualitative properties as in the full EinsteinHilbert truncation. In particular it possesses the nonGaussian fixed point which is necessary for asymptotic safety.},
doi = {10.1103/PHYSREVD.79.105005},
url = {https://www.osti.gov/biblio/21296368},
journal = {Physical Review. D, Particles Fields},
issn = {05562821},
number = 10,
volume = 79,
place = {United States},
year = {2009},
month = {5}
}