Spectral dimensions from the spectral action

Abstract

The generalised spectral dimension $D_S(T)$ provides a powerful tool for comparing different approaches to quantum gravity. In this work, we apply this formalism to the classical spectral actions obtained within the framework of almost-commutative geometry. Analysing the propagation of spin-0, spin-1 and spin-2 fields, we show that a non-trivial spectral dimension arises already at the classical level. The effective field theory interpretation of the spectral action yields plateau-structures interpolating between a fixed spin-independent $D_S(T)=d_S$ for short and $D_S(T)=4$ for long diffusion times $T$. Going beyond effective field theory the spectral dimension is completely dominated by the high-momentum properties of the spectral action, yielding $D_S(T)=0$ for all spins. Our results support earlier claims that high-energy bosons do not propagate.

9 pages, 3 figures; version to be published in Physical Review D

References in corpus (11)

• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Fractal properties of quantum spacetime
• Noncommutative Geometry and the standard model with neutrino mixing
• Resilience of the Spectral Standard Model
• Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model
• Constraining the Noncommutative Spectral Action via Astrophysical Observations
• Diffusion on $\kappa$-Minkowski space
• On the non-local heat kernel expansion
• Vacuum Fluctuations and the Small Scale Structure of Spacetime
• Particle Physics from Almost Commutative Spacetimes
• Renormalization of the spectral action for the Yang-Mills system

Cited by in corpus (5)

• Dimension and Dimensional Reduction in Quantum Gravity
• Spectral action with zeta function regularization
• The disappearance of causality at small scale in almost-commutative manifolds
• Dimensional Deception from Noncommutative Tori: An alternative to Horava-Lifschitz
• Primordial black holes in a dimensionally oxidizing Universe