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.