A tale of two actions a variational principle for two-dimensional causal sets

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]. (paper)