Asymptotic Safety of Four-Dimensional Quantum Gravity

Determine whether quantum gravity in four spacetime dimensions is asymptotically safe by establishing that the renormalization group flow of all gravitational couplings approaches a finite-dimensional ultraviolet critical surface, thereby ensuring predictivity at arbitrarily high energies.

Background

Weinberg conjectured that some quantum field theories, including gravity, might be asymptotically safe, meaning their couplings flow to a finite-dimensional manifold in the ultraviolet, preserving predictivity. This would provide a quantum field theoretic resolution to gravity’s nonrenormalizability without requiring new degrees of freedom.

The authors explicitly state that the status of asymptotic safety in four dimensions remains controversial due to current calculational limitations, underscoring the need for decisive theoretical or computational evidence to confirm or refute the conjecture in the physically relevant case.

References

It remains controversial whether gravity in 4 spacetime dimensions is actually asymptotically safe (our main calculational tools are restricted to the low-energy and weak-curvature regime), but if it were then standard QFT techniques could suffice to describe gravity in the strongly quantum domain (and thereby provide the simplest approach to making sensible predictions for it at high energies).

— Steven Weinberg: A Scientific Life  (2502.10979 - Burgess et al., 16 Feb 2025) in Section 2.3, 1970s — Asymptotic Safety

The question of whether a different treatment of the off-shell pole in the metric propagator can give rise to a Horndeski trajectory with positive $\Lambda$ in the IR is left to future work.

— Emergence of Horndeski gravity from asymptotic safety?  (2609.29369 - Eichhorn et al., 24 Sep 2026) in Section 2, subsection “Results: Horndeski coupling ratio for universes with tiny |Λ|”

The question of whether Horndeski gravity can be ruled out as the EFT approximation to asymptotically safe scalar-tensor theories becomes even more nontrivial in larger truncations, and this work highlights the importance of further investigation of this issue.

— Emergence of Horndeski gravity from asymptotic safety?  (2609.29369 - Eichhorn et al., 24 Sep 2026) in Section 5, Conclusion and outlook