Monotonicity of the dimensionless Newton coupling in FRG flows

Determine whether the dimensionless Newton coupling g_k is monotonic in the renormalisation group scale k across functional renormalisation group computations of quantum gravity, and identify the truncations and regulator choices under which monotonicity holds, to justify rescaling strategies that rely on this property.

Background

When discussing numerical strategies for solving momentum-dependent flows, the authors note that certain rescalings using the running gravitational coupling may fail if g_k is not monotonic in k. They state that monotonicity is not guaranteed in general and may fail in many computations.

Establishing conditions for monotonicity is important for robust numerical implementations that convert dimensionful to dimensionless variables using g_k.

References

The latter is the case in many computations, and in general it is not known a priori whether g_k is indeed monotonic.

— Asymptotically (un)safe scattering amplitudes from scratch: a deep dive into the IR jungle  (2602.21285 - Knorr, 24 Feb 2026) in Section 6, Numerics (footnote)