On the continuum limit of Benincasa-Dowker-Glaser causal set action
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.
Keywords
Cite
@article{arxiv.2007.13192,
title = {On the continuum limit of Benincasa-Dowker-Glaser causal set action},
author = {Ludovico Machet and Jinzhao Wang},
journal= {arXiv preprint arXiv:2007.13192},
year = {2020}
}
Comments
26 pages (including cover page), 2 figures. We expect an independent work on the same topic by Fay Dowker to be submitted to the ArXiv at the same time of this work. Cross reference to this work added in version 2