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: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
Truncated functional renormalization group studies since Reuter (1998) find a fixed point; convergence, Lorentzian formulation and unitarity remain disputed as of 2026.
Parent problems
- Special case of Which theory completes general relativity at the Planck scale? · open · from revision 1 The parent was revised since revision 1: it now states another question.
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