Dimensional reduction in manifold-like causal sets

TL;DR

This paper studies how small subsets of causal sets approximating Minkowski space exhibit a decrease in effective dimension at short distances, with the minimum dimension around 2, aligning with other quantum gravity approaches.

Contribution

It demonstrates that the effective dimension of causal sets reduces at small scales and explores the dependence on different dimensional estimators.

Findings

Effective dimension decreases smoothly at small distances.

Minimum dimension around 2 for Myrheim-Meyer estimator.

Results consistent with other quantum gravity models.

Abstract

We investigate the behavior of small subsets of causal sets that approximate Minkowski space in three, four, and five dimensions, and show that their effective dimension decreases smoothly at small distances. The details of the short distance behavior depend on a choice of dimensional estimator, but for a reasonable version of the Myrheim-Meyer dimension, the minimum dimension is $d \approx 2$, reproducing results that have been seen in other approaches to quantum gravity.