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

References in corpus (8)

• Cosmology of the Lifshitz universe
• Fractal properties of quantum spacetime
• Discreteness without symmetry breaking: a theorem
• Diffusion on $\kappa$-Minkowski space
• Generalized Causal Set d'Alembertians
• Nonlocal Scalar Quantum Field Theory from Causal Sets
• Dimensional reduction in causal set gravity
• Dark Matter From Spacetime Nonlocality

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• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
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