Evidence for Asymptotic Safety from Dimensional Reduction in Causal Dynamical Triangulations

TL;DR

This paper demonstrates that the spectral dimension in causal dynamical triangulations decreases from 4 to 1.5 at small scales, supporting the asymptotic safety scenario in quantum gravity and introducing a method to determine lattice spacing.

Contribution

It provides nonperturbative evidence for dimensional reduction in CDT and proposes a new approach to measure lattice spacing relevant for quantum gravity studies.

Findings

Spectral dimension decreases from 4 to 1.5 at small scales.

Supports the asymptotic safety scenario in quantum gravity.

Introduces a method to determine lattice spacing in CDT.

Abstract

We calculate the spectral dimension for a nonperturbative lattice approach to quantum gravity, known as causal dynamical triangulations (CDT), showing that the dimension of spacetime smoothly decreases from approximately 4 on large distance scales to approximately 3/2 on small distance scales. This novel result may provide a possible resolution to a long-standing argument against the asymptotic safety scenario. A method for determining the relative lattice spacing within the physical phase of the CDT parameter space is also outlined, which might prove useful when studying renormalization group flow in models of lattice quantum gravity.