Determine whether the dephasing scale greatly exceeds the nonlocality scale in realistic settings

Ascertain whether the holographic dephasing length scale ℓΛ, on which the phase factors oscillate, is indeed much larger than the nonlocality length scale ℓmin of the potentials in physically realistic causal fermion systems; if so, quantify this separation, and if not, analyze implications for the perturbative and microlocal expansions relying on this assumption.

Background

Several computational techniques in the paper—such as perturbative resummations and microlocal expansions—rely on a hierarchy of length scales, in particular the assumption ℓΛ ≫ ℓmin. This separation facilitates treating rapidly oscillating holographic phase factors non-perturbatively while expanding in powers of ℓmin/ℓΛ.

The authors explicitly note that it is currently unclear whether this hierarchy holds in physically realistic situations, affecting the generality and applicability of the presented methods.