Asymptotically safe quantum gravity: functional and lattice perspectives

TL;DR

The paper argues that asymptotically safe quantum gravity (ASQG) could unify gravity with the Standard Model by realizing quantum scale symmetry at a UV fixed point. It reviews two nonperturbative approaches, the functional renormalization group using the scale-dependent action $\\Gamma_k$ and the Wetterich equation, and lattice methods based on Dynamical Triangulations (DT) and its causal variant CDT, highlighting their complementary strengths. FRG findings reveal a nontrivial UV fixed point with $G_*>0$ and finite $\\lambda_*$, robust across truncations and matter content, with gravitational anti-screening in Abelian sectors potentially producing a UV-attractive hypercharge fixed point $g_{y,*}>0$ and enabling SM UV completion. The lattice DT/CDT results show phase structure and geometries compatible with a continuum limit and hints of a Reuter fixed point, strengthening confidence in ASQG as a UV-complete framework. Overall, the combination suggests ASQG could provide predictive UV completion and possibly fix certain SM parameters, with future work focusing on gravity-matter systems and cross-validation between FRG and lattice results.

Abstract

Asymptotically safe quantum gravity is a candidate theory to quantum gravity, which could unify the gravitational interaction with particle physics. It is characterized by quantum scale-symmetry at high energies. The constraining power of scale symmetry could be strong enough to even explain some parameters of the Standard Model of particle physics from first principles.