态密度与CKN界
Densities of States and the CKN Bound
摘要：
全息原理意味着量子场论过多地计算了量子引力中的独立自由度。科恩、卡普兰和纳尔逊（Cohen，Kaplan，and Nelson，CKN）的一个论点表明，QFT所描述的自由度的数量甚至比全息边界所要求的还要小，CKN将这一结果解释为QFT上紫外和红外截止点之间的相关性。在这里，我们考虑另一种解释，其中QFT的自由度被耗尽作为规模的函数。我们使用一个简单的配方来估计耗尽态密度对精确观测的影响，包括兰姆位移和轻子$g-2$。虽然这些观测量对引力引起的损耗水平并不敏感，但唯象学的实验也提供了一个有趣的测试，即独立于基本的量子引力假设的量子场论。耗尽态密度也可以使QFT真空能量对紫外线不敏感，调和了QFT在描述普通粒子物理过程方面的成功和在预测宇宙学常数方面的明显失败。
英文摘要：
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.
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