On the continuum limit of Benincasa-Dowker-Glaser causal set action

Ludovico Machet; Jinzhao Wang

doi:10.1088/1361-6382/abc274

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arXiv · 2007.13192

On the continuum limit of Benincasa-Dowker-Glaser causal set action

Ludovico Machet·Jinzhao Wang

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Abstract

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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Ludovico Machet, Jinzhao Wang. 2020-07-28. On the continuum limit of Benincasa-Dowker-Glaser causal set action. https://doi.org/10.1088/1361-6382%2Fabc274

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