Densities of States and the CKN Bound

TL;DR

This paper explores how a depletion of quantum field theory degrees of freedom at different scales can reconcile QFT with gravitational bounds and address the cosmological constant problem, while testing its effects on precision measurements.

Contribution

It proposes a scale-dependent depletion model of QFT degrees of freedom and examines its implications for observable phenomena and the cosmological constant.

Findings

Depleted densities of states have minimal impact on Lamb shift and lepton g-2.

The depletion model makes QFT vacuum energy UV-insensitive.

Results suggest a potential resolution to the cosmological constant problem.

Abstract

The holographic principle implies that quantum field theory overcounts the number of independent degrees of freedom in quantum gravity. An argument due to Cohen, Kaplan, and Nelson (CKN) suggests that the number of degrees of freedom well-described by QFT is even smaller than required by holographic bounds, and CKN interpreted this result as indicative of a correlation between the UV and IR cutoffs on QFT. Here we consider an alternative interpretation in which the QFT degrees of freedom are depleted as a function of scale. We use a simple recipe to estimate the impact of depleted densities of states on precision observables, including the Lamb shift and lepton $g-2$. Although these observables are not sensitive to the level of depletion motivated by gravitational considerations, the phenomenological exercises also provide an interesting test of quantum field theory that is independent of underlying quantum gravity assumptions. A depleted density of states can also render the QFT vacuum energy UV-insensitive, reconciling the success of QFT in describing ordinary particle physics processes and its apparent failure in predicting the cosmological constant.