We study the continuum limit of the Benincasa-Dowker-Glaser causal set action on a causally convex compact region. In particular, we compute the action of a causal set randomly sprinkled on a small causal diamond in the presence of arbitrary curvature in various spacetime dimensions. In the continuum limit, we show that the action admits a finite limit. More importantly, the limit is composed by an Einstein-Hilbert bulk term as predicted by the Benincasa-Dowker-Glaser action, and a boundary term exactly proportional to the codimension-two joint volume. Our calculation provides strong evidence in support of the conjecture that the Benincasa-Dowker-Glaser action naturally includes codimension-two boundary terms when evaluated on causally convex regions.

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关于 Benincasa-Dowker-Glaser 因果集作用的连续统极限

我们研究了 Benincasa-Dowker-Glaser 因果集作用在因果凸紧凑区域上的连续统极限。特别是，我们计算了在各种时空维度中存在任意曲率的情况下随机洒在一个小的因果菱形上的因果集的作用。在连续体极限中，我们证明动作承认有限极限。更重要的是，该极限由由 Benincasa-Dowker-Glaser 作用预测的爱因斯坦-希尔伯特体项和与二次维-二联合体积成正比的边界项组成。我们的计算提供了强有力的证据来支持这样的猜想，即当在因果凸区域上进行评估时，Benincasa-Dowker-Glaser 作用自然包括二维边界项。