Dimensionally Restricted Causal Sets

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We study dimensionally restricted non-perturbative causal set quantum dynamics in two and three spacetime dimensions with non-trivial global spatial topology.  The causal set sample space is generated from causal embeddings into latticisations of flat background spacetimes with global spatial topology S^1 and T^2 in two and three dimensions, respectively. The quantum gravity partition function over these sample spaces is studied using Markov Chain Monte Carlo (MCMC) simulations via an analytic continuation of a parameter \beta analogous to an inverse temperature. In both two and three dimensions we find a phase transition that separates the dominance of the action from that of the entropy. The action dominated phase is characterised by "layered" posets with a high degree of connectivity, while the causal sets in the entropy dominated phase are manifold-like. These results are similar in character to those obtained for topologically trivial causal set dynamics over the sample space of 2-orders. The current simulations use a newly developed framework for causal set MCMC calculations, and provide the first implementation of a three-dimensional causal set dynamics.


arXiv paper: https://arxiv.org/abs/1908.11647