Spectral Dimension from Nonlocal Dynamics on Causal Sets

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.

7 pages, 2 figures, version accepted for publication in Phys. Rev. D