GRAV In the literature: contested

Does 4D quantum gravity with matter have an ultraviolet fixed point?

In plain words

Asymptotic safety proposes that gravity stops getting stronger at short distances because the theory approaches a scale-invariant point, called a fixed point. The evidence comes from approximate calculations whose reliability is debated.

Precise statement

For the renormalization group flow of 4D gravity coupled to Standard Model matter, determine whether a non-Gaussian fixed point exists with finitely many UV-relevant directions, beyond truncations of the effective action, in Lorentzian signature and without ghosts in the full graviton propagator. An answer is a controlled demonstration (for example convergence across systematically enlarged truncations, or a lattice continuum limit) or a no-go result.

What would settle it

Convergence of fixed-point properties under systematic enlargement of truncations, confirmed by an independent non-perturbative method.

Status in the literature

Unverified note

Truncated functional renormalization group studies since Reuter (1998) find a fixed point; convergence, Lorentzian formulation and unitarity remain disputed as of 2026.