Dimensional reduction in causal set gravity

TL;DR

This paper demonstrates that multiple dimension estimators in causal set theory indicate a dimensional reduction to two dimensions at small scales, suggesting a phenomenon akin to asymptotic silence in quantum gravity.

Contribution

The paper shows consistent dimensional reduction across different estimators in causal set theory and introduces the idea of asymptotic silence related to spectral dimension behavior.

Findings

Dimensional estimators in causal set theory suggest d=2 at small scales.

Spectral dimension may exhibit asymptotic silence.

Supports the idea of dimensional reduction in quantum gravity models.

Abstract

Results from a number of different approaches to quantum gravity suggest that the effective dimension of spacetime may drop to $d=2$ at small scales. I show that two different dimensional estimators in causal set theory display the same behavior, and argue that a third, the spectral dimension, may exhibit a related phenomenon of "asymptotic silence."