Quantizing gravity within the framework of quantum field theory remains an open challenge in modern theoretical physics. One potential solution to this issue is the asymptotic safety mechanism proposed by Weinberg. The core idea of the asymptotic safety program is that a non-Gaussian fixed point (NGFP) of the renormalization group (RG) flow governs gravity in the high-energy regime, rendering the theory free of UV divergences. The existence of such a NGFP has been confirmed in various works using different truncations of the gravitational effective average action (EAA) on Euclidean spacetime.
This thesis investigates two important aspects of the asymptotic safety program: the reliability of truncations and the inclusion of Lorentzian signature. First, it clarifies the dependence of the NGFP on the unphysical elements of truncations in gravity-matter systems. Next, it implements the analytic continuation from Euclidean to Lorentzian spacetime by considering a foliation structure of spacetime. The results open the possibility to formally prove the equivalence between the Lorentzian and Euclidean asymptotic safety programs.
Jian Wang was born in Hebei, China in 1993. From 2012 to 2019, Jian studied theoretical physics at Lanzhou University in Gansu, China. After he got his master’s degree in 2019, Jian received a scholarship and started his PhD under the supervision of prof. dr. R. Loll and dr. F. Saueressig at Radboud University in the Netherlands. During his PhD, Jian worked on several projects in asymptotically safe quantum gravity.