Generalised spectral dimensions in non-perturbative quantum gravity

TL;DR

This paper investigates how the effective spectral dimension in non-perturbative quantum gravity models varies with different field types, revealing that some fields exhibit a flow between scales while others do not, impacting quantum gravity phenomenology.

Contribution

It extends the study of spectral dimensions in quantum gravity to $k$-form fields, showing field-dependent behavior near the Planck scale.

Findings

Two-form, tensor, and dual scalar spectral dimensions show a flow between scales.

One-form and vector spectral dimensions exhibit only a single effective dimension.

Field-dependent spectral dimension behavior may relate to the presence or absence of dispersion relations.

Abstract

The seemingly universal phenomenon of scale-dependent effective dimensions in non-perturbative theories of quantum gravity has been shown to be a potential source of quantum gravity phenomenology. The scale-dependent effective dimension from quantum gravity has only been considered for scalar fields. It is however possible that the non-manifold like structures, that are expected to appear near the Planck scale, have an effective dimension that depends on the type of field under consideration. To investigate this question, we have studied the spectral dimension associated to the Laplace-Beltrami operator generalised to $k$-form fields on spatial slices of the non-perturbative model of quantum gravity known as Causal Dynamical Triangulations. We have found that the two-form, tensor and dual scalar spectral dimensions exhibit a flow between two scales at which an effective dimension appears. However, the one-form and vector spectral dimensions show only a single effective dimension. The fact that the one-form and vector spectral dimension do not show a flow of the effective dimension can potentially be related to the absence of a dispersion relation for the electromagnetic field, but dynamically generated instead of as an assumption.