标题： 熵主导因果集的爱因斯坦-希尔伯特作用量 显示英文标题

标题： The Einstein-Hilbert Action for Entropically Dominant Causal Sets

摘要： 在因果集量子引力的路径积分表述中，量子配分函数是局部有限的部分有序集的相位加权和，这些集被看作离散的量子时空。 然而，已知“分层”集——一类与时空流形毫无相似之处的因果集——的数量随着基数$n$的增长呈超指数增长，这会带来一个可能超过作用量贡献的熵贡献。 我们在此证明，在任何维度下，典型$K$分层因果集的离散爱因斯坦-希尔伯特作用量在$n$的高阶项下简化为简单的链接作用量。 结合之前的工作，这完成了证明：尽管分层集在熵上占主导地位，但只要离散化尺度大于或等于普朗克尺度的一个（略微依赖维度的）常数倍，它们在因果集量子引力的路径求和中会被强烈抑制。 显示英文摘要

摘要： In the path integral formulation of causal set quantum gravity, the quantum partition function is a phase-weighted sum over locally finite partially ordered sets, which are viewed as discrete quantum spacetimes. It is known, however, that the number of ``layered'' sets -- a class of causal sets that look nothing like spacetime manifolds -- grows superexponentially with the cardinality $n$, giving an entropic contribution that can potentially dominate that of the action. We show here that in any dimension, the discrete Einstein-Hilbert action for a typical $K$-layered causal set reduces to the simple link action to leading order in $n$. Combined with earlier work, this completes the proof that the layered sets, although entropically dominant, are very strongly suppressed in the path sum of causal set quantum gravity whenever the discreteness scale is greater than or equal to a (mildly dimension-dependent) order one multiple of the Planck scale.