Spectral Dimension from Nonlocal Dynamics on Causal Sets

TL;DR

This paper explores how non-local continuum d'Alembertians derived from causal sets lead to a universal reduction of spectral dimension to 2, regardless of the original dimension, impacting quantum field theory models.

Contribution

It demonstrates a universal spectral dimension reduction to 2 from non-local causal set dynamics across all dimensions, providing insights into quantum gravity models.

Findings

Spectral dimension reduces to 2 in all dimensions

Universal behavior observed in non-local causal set models

Implications for quantum field theories with nonlocal dynamics

Abstract

We investigate the spectral dimension obtained from non-local continuum d'Alembertians derived from causal sets. We find a universal dimensional reduction to 2 dimensions, in all dimensions. We conclude by discussing the validity and relevance of our results within the broader context of quantum field theories based on these nonlocal dynamics.