In this paper we will explore two different proposals for the action for causal sets: the Benincasa–Dowker action [1], and a modified version of the chain action [2]. We propose a variational principle for two-dimensional causal sets and use it for both actions to determine which causal sets at least on average satisfy a discrete version of the Einstein equation. Specifically, we test this method on causal sets embedded in 2d Minkowski, de Sitter, and anti-de Sitter spacetimes and compare the results with those obtained for the most prominent nonmanifoldlike causal sets, the Kleitman–Rothschild causal sets [3].

在本文中，我们将探讨因果集动作的两种不同建议：Benincasa-Dowker 动作 [1] 和链式动作的修改版本 [2]。我们提出了二维因果集的变分原理，并将其用于两个动作，以确定哪些因果集至少平均满足爱因斯坦方程的离散版本。具体来说，我们在嵌入 2d Minkowski、de Sitter 和 anti-de Sitter 时空的因果集上测试这种方法，并将结果与​​最突出的非流形因果集 Kleitman-Rothschild 因果集 [3] 的结果进行比较。