  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.

General Relativity and Quantum Cosmology;High Energy Physics - Theory