Renormalization group equation for [function] (R) gravity on hyperbolic spaces

• Verfasst von: Falls, Kevin [VerfasserIn]
• Verfasst von: Ohta, Nobuyoshi [VerfasserIn]
• Titel: Renormalization group equation for [function] (R) gravity on hyperbolic spaces
• Verf.angabe: Kevin Falls and Nobuyoshi Ohta
• E-Jahr: 2016
• Jahr: 4 October 2016
• Umfang: 20 S.
• Fussnoten: Titel ist "function" als mathematisches Zeichen dargestellt ; Gesehen am 13.05.2020
• Titel Quelle: Enthalten in: Physical review
• Ort Quelle: Woodbury, NY : Inst., 2016
• Jahr Quelle: 2016
• Band/Heft Quelle: 94(2016,8) Artikel-Nummer 084005, 20 Seiten
• ISSN Quelle: 2470-0029
• DOI: doi:10.1103/PhysRevD.94.084005
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1698100779

Abstract

We derive the flow equation for the gravitational effective average action in an f(R) truncation on hyperbolic spacetimes using the exponential parametrization of the metric. In contrast to previous works on compact spaces, we are able to evaluate traces exactly using the optimized cutoff. This reveals in particular that all modes can be integrated out for a finite value of the cutoff due to a gap in the spectrum of the Laplacian, leading to the effective action. Studying polynomial solutions, we find poorer convergence than has been found on compact spacetimes even though at small curvature the equations only differ in the treatment of certain modes. In the vicinity of an asymptotically free fixed point, we find the universal beta function for the R2 coupling and compute the corresponding effective action which involves an R2log(R2) quantum correction.