Abstract
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 $g\ensuremath{-}2$. 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.
Highlights
We do not know how realistic quantum field theories emerge as a low-energy approximation to a complete theory of quantum gravity with a positive cosmological constant
In quantum field theory (QFT), the maximum entropy localized in a box of size L scales extensively as S ∼ ðΛLÞ3, while the holographic principle limits the number of degrees of freedom in quantum gravity to S ∼ M2pL2
This overabundance of QFT states does not mean that most of the states in quantum gravity have to behave like bulk QFT states
Summary
We do not know how realistic quantum field theories emerge as a low-energy approximation to a complete theory of quantum gravity with a positive cosmological constant (cc). In QFT, the maximum entropy localized in a box of size L scales extensively as S ∼ ðΛLÞ3, while the holographic principle limits the number of degrees of freedom in quantum gravity to S ∼ M2pL2. We see that the partonic model realizes the holographic principle by a scale-dependent depletion of the independent degrees of freedom, relative to the density of states of an ordinary bulk field theory in a fixed volume. [10], where 1=L is taken to be a bound on a characteristic momentum spacing between independent degrees of freedom that can be well described by bulk quantum field theory. Since no real experiment is sensitive to arbitrarily small differences in momenta or energy, there are only empirical lower bounds on the QFT single-particle density of states. We will conclude that the bounds on the DOS obtained from precision particle physics measurements are far from definitively establishing that the cc problem is a problem, without invoking a substantial extrapolation
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