Infrared behavior of Weyl gravity: Functional renormalization group approach

Petr Jizba, Lesław Rachwał, Jaroslav Kňap
2020 Physical Review D  
Starting from ultraviolet fixed point we study infrared behavior of quantum Weyl gravity in terms of functional RG flow equation. To do so, we employ two classes of Bach-flat backgrounds, namely maximally symmetric spacetimes and Ricci-flat backgrounds in the improved one-loop scheme. We show, that in the absence of matter fields and with a topological term included, the effective action exhibits dynamical breaking of scale symmetry. In particular, it is shown that apart from genuine IR fixed
more » ... genuine IR fixed point that is reached at zero-value of the running scale, the RG flow also exhibits bouncing behavior in the IR regime. We demonstrate that both $\beta_C$ and $\beta_E$ reach the RG turning point (almost) simultaneously at the same finite energy scale, irrespectively of the chosen background. The IR fixed point itself is found to be IR-stable in the space of considered couplings. Ensuing scaling dimensions of both operators are also computed. Salient issues, including connection of the observed bouncing RG flow behavior with holography and prospective implications in early universe cosmology are also briefly discussed.
doi:10.1103/physrevd.101.044050 fatcat:pbbgvqs2afballvx4idzgimcam