Dimensional reduction in causal set gravity

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."

6+1 pages; v2: added references, cite of new result on spectral dimension; v3: minor corrections to match published version

References in corpus (11)

• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Fractal properties of quantum spacetime
• Discreteness without symmetry breaking: a theorem
• Feynman Propagator for a Free Scalar Field on a Causal Set
• Diffusion on $\kappa$-Minkowski space
• Generalized Causal Set d'Alembertians
• Spacelike distance from discrete causal order
• Nonlocal Scalar Quantum Field Theory from Causal Sets
• Vacuum Fluctuations and the Small Scale Structure of Spacetime
• High temperature dimensional reduction in Snyder space
• The Discrete Geometry of a Small Causal Diamond

Cited by in corpus (26)

• Upper bound on the Abelian gauge coupling from asymptotic safety
• Quantum Gravity signatures in the Unruh effect
• Spectral Dimension from Nonlocal Dynamics on Causal Sets
• Is scale-invariance in gauge-Yukawa systems compatible with the graviton?
• Towards the map of quantum gravity
• Noncommutative fields and the short-scale structure of spacetime
• Thermal dimension of quantum spacetime
• Spontaneous Dimensional Reduction in Quantum Gravity
• Raychaudhuri equation with zero point length
• Signal propagation on $\kappa$-Minkowski spacetime and non-local two-point functions
• Quantum Gravity on the computer: Impressions of a workshop
• Spectral dimension with deformed spacetime signature
• Spectral dimensions and dimension spectra of quantum spacetimes
• On characterizing the Quantum Geometry underlying Asymptotic Safety
• Dimensional reduction in manifold-like causal sets
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Extrinsic curvature in 2-dimensional Causal Dynamical Triangulation
• Pre-big bang geometric extensions of inflationary cosmologies
• Ultraviolet dimensional reduction of spacetime with zero-point length
• Modified dispersion relations, inflation and scale invariance
• UV dimensional reduction to two from group valued momenta
• Primordial black holes in a dimensionally oxidizing Universe
• Thermal and spectral dimension of (generalized) Snyder noncommutative spacetimes
• A general theorem on temporal foliation of causal sets
• Local Structure of Sprinkled Causal Sets
• Quantum Field Theory on Multifractal Spacetime: Varying Dimension and Ultraviolet Completeness