A Perturbative Window into Asymptotic Safety

Abstract

Asymptotic safety offers a compelling UV completion of quantum gravity through a non-trivial UV fixed point. Evidence for this has so far come predominantly from the functional renormalization group. In this talk, I explore a complementary perturbative approach, which offers manifest gauge invariance and allows for computations directly in Lorentzian signature. A crucial ingredient for this is the use of renormalization schemes that are not mass-independent but retain sensitivity to power-law effects. Two realizations of this idea are discussed: a variant of dimensional regularization that goes beyond minimal subtraction, and an adaptation of gradient-flow techniques that have proven successful in QCD. As a proof of concept, I show that in QCD these ideas capture effects that would otherwise be missed, such as the decoupling of heavy quarks. Applying the same methods to gravity, I find that a UV fixed point already emerges at one-loop, with indications that it lies within a perturbative domain. I close by comparing these findings with functional renormalization group results on asymptotic safety and discussing future directions.