The holographic principle implies that quantum field theory (QFT) 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.

中文翻译：

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状态密度和 Cohen-Kaplan-Nelson 界

全息原理意味着量子场论 (QFT) 夸大了量子引力中独立自由度的数量。Cohen、Kaplan 和 Nelson (CKN) 提出的一个论点表明，QFT 所描述的自由度数甚至比全息边界所要求的还要小，CKN 将这一结果解释为 UV 和 IR 截止点之间的相关性在 QFT 上。在这里，我们考虑另一种解释，其中 QFT 自由度作为尺度的函数耗尽。我们使用一个简单的方法来估计耗尽态密度对精确可观测值的影响，包括兰姆位移和轻子$G-2$. 尽管这些可观测值对由引力考虑引起的损耗水平不敏感，但现象学练习也提供了一个有趣的量子场论测试，该测试独立于潜在的量子引力假设。耗尽的态密度也可以使 QFT 真空能量 UV 不敏感，这将 QFT 在描述普通粒子物理过程方面的成功与其在预测宇宙常数方面的明显失败相协调。