Construction of Causal Set Propagators in 2+1-Dimensional Constant-Curvature Spacetimes from Two-Link Paths
Abstract
We study a link-based retarded scalar propagator on causal sets sprinkled into 2+1-dimensional Minkowski, anti-de Sitter, and de Sitter spacetimes. The construction is based on the squared link matrix L2, whose expectation value counts two-link paths between fixed endpoints. In the high-density limit, the dominant contribution localizes near the intersection of the null boundaries of the Alexandrov interval, and the flat-space normalization remains unchanged in constant curvature. The resulting kernels agree with the corresponding continuum Klein-Gordon propagators for a nominally massless scalar with effective curvature coupling ξlink=1/6. Since the conformal coupling in 2+1 spacetime dimensions is 1/8, this value is not a conformal-coupling effect. Together with link-based results in 1+1 and 3+1 dimensions, where the same coefficient 1/6 appears, this suggests that the coupling may reflect an ultraviolet property of the link structure, reminiscent of the combination (1/6−ξ)ℛ in local heat-kernel expansions.
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BibTeX
@misc{kastrati2026construction,
title = {{Construction of Causal Set Propagators in $2+1$-Dimensional Constant-Curvature Spacetimes from Two-Link Paths}},
author = {Arsim Kastrati},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26221},
eprint = {2610.26221},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26221},
}
RIS
TY - UNPB
TI - Construction of Causal Set Propagators in 2+1-Dimensional Constant-Curvature Spacetimes from Two-Link Paths
AU - Arsim Kastrati
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26221
UR - https://arxiv.org/abs/2610.26221
AB - We study a link-based retarded scalar propagator on causal sets sprinkled into 2+1-dimensional Minkowski, anti-de Sitter, and de Sitter spacetimes. The construction is based on the squared link matrix L^2, whose expectation value counts two-link paths between fixed endpoints. In the high-density limit, the dominant contribution localizes near the intersection of the null boundaries of the Alexandrov interval, and the flat-space normalization remains unchanged in constant curvature. The resulting kernels agree with the corresponding continuum Klein-Gordon propagators for a nominally massless scalar with effective curvature coupling ξ_link=1/6. Since the conformal coupling in 2+1 spacetime dimensions is 1/8, this value is not a conformal-coupling effect. Together with link-based results in 1+1 and 3+1 dimensions, where the same coefficient 1/6 appears, this suggests that the coupling may reflect an ultraviolet property of the link structure, reminiscent of the combination (1/6−ξ)ℛ in local heat-kernel expansions.
ER -