Many real-world networks are embedded into a space or spacetime. The embedding space(time) constrains the properties of these real-world networks. We use the scale-dependent spectral dimension as a tool to probe whether real-world networks encode inf
ormation on the dimensionality of the embedding space. We find that spacetime networks which are inspired by quantum gravity and based on a hybrid signature, following the Minkowski metric at small spatial distance and the Euclidean metric at large spatial distance, provide a template relevant for real-world networks of small-world type, including a representation of the internets architecture and biological neural networks.
We discover a weak-gravity bound in scalar-gravity systems in the asymptotic-safety paradigm. The weak-gravity bound arises in these systems under the approximations we make, when gravitational fluctuations exceed a critical strength. Beyond this cri
tical strength, gravitational fluctuations can generate complex fixed-point values in higher-order scalar interactions. Asymptotic safety can thus only be realized at sufficiently weak gravitational interactions. We find that within truncations of the matter-gravity dynamics, the fixed point lies beyond the critical strength, unless spinning matter, i.e., fermions and vectors, is also included in the model.
The Renormalization Group encodes three concepts that could be key to accelerate progress in quantum gravity. First, it provides a micro-macro connection that could connect microscopic spacetime physics to phenomenology at observationally accessible
scales. Second, it enables a search for universality classes that could link diverse quantum-gravity approaches and allow us to discover that distinct approaches could encode the same physics in mathematically distinct structures. Third, it enables the emergence of symmetries at fixed points of the Renormalization Group flow, providing a way for spacetime symmetries to emerge from settings in which these are broken at intermediate steps of the construction. These three concepts make the Renormalization Group an attractive method and conceptual underpinning of quantum gravity. Yet, in its traditional setup as a local coarse-graining, it could appear at odds with concepts like background independence that are expected of quantum gravity. Within the last years, several approaches to quantum gravity have found ways how these seeming contradictions could be reconciled and the power of the Renormalization Group approach unleashed in quantum gravity. This special issue brings together research papers and reviews from a broad range of quantum gravity approaches, providing a partial snapshot of this evolving field.
Quantum Gravity is expected to resolve the singularities of classical General Relativity. Based on destructive interference of singular spacetime-configurations in the path integral, we find that higher-order curvature terms may allow to resolve blac
k-hole singularities both in the spherically symmetric and axisymmetric case. In contrast, the Einstein action does not provide a dynamical mechanism for singularity-resolution through destructive interference of these configurations.
The question whether global symmetries can be realized in quantum-gravity-matter-systems has far-reaching phenomenological consequences. Here, we collect evidence that within an asymptotically safe context, discrete global symmetries of the form $mat
hbb{Z}_n$, $n>4$, cannot be realized in a near-perturbative regime. In contrast, an effective-field-theory approach to quantum gravity might feature such symmetries, providing a mechanism to generate mass hierarchies in the infrared without the need for additional fine-tuning.
We study the impact of quantum gravity on a system of chiral fermions that are charged under an Abelian gauge group. Under the impact of quantum gravity, a finite value of the gauge coupling could be generated and in turn drive four-fermion interacti
ons to criticality. We find indications that the gravity-gauge-fermion interplay protects the lightness of fermions for a large enough number of fermions. On the other hand, for a smaller number of fermions, chiral symmetry may be broken, which would be in tension with the observation of light fermions.
We calculate the gravitational-wave spectra produced by the electroweak phase transition with TeV-scale Beyond-Standard-Model physics in the early universe. Our study captures the effect of quantum and thermal fluctuations within a non-perturbative f
ramework. We discover a universal relation between the mean bubble separation and the strength parameter of the phase transition, which holds for a wide range of new-physics contributions. The ramifications of this result are three-fold: First, they constrain the gravitational-wave spectra resulting from heavy (TeV-scale) new physics. Second, they contribute to distinguishing heavy from light new physics directly from the gravitational-wave signature. Third, they suggest that a concerted effort of gravitational-wave observations together with collider experiments could be required to distinguish between different models of heavy new physics.
Asymptotic safety is a theoretical proposal for the ultraviolet completion of quantum field theories, in particular for quantum gravity. Significant progress on this program has led to a first characterization of the Reuter fixed point. Further advan
cement in our understanding of the nature of quantum spacetime requires addressing a number of open questions and challenges. Here, we aim at providing a critical reflection on the state of the art in the asymptotic safety program, specifying and elaborating on open questions of both technical and conceptual nature. We also point out systematic pathways, in various stages of practical implementation, towards answering them. Finally, we also take the opportunity to clarify some common misunderstandings regarding the program.
We explore a simple parameterization of new physics that results in an ultraviolet complete gauge-quark sector of the Standard Model. Specifically, we add an antiscreening contribution to the beta functions of the gauge couplings and a flavor-indepen
dent, antiscreening contribution to the beta functions of the Yukawa couplings. These two free parameters give rise to an intricate web of Renormalization Group fixed points. Their predictive power extends to the flavor structure and mixing patterns, which we investigate to demonstrate that some of the free parameters of the Standard Model could be determined by the Renormalization Group flow.
This is an introduction to asymptotically safe quantum gravity, explaining the main idea of asymptotic safety and how it could solve the problem of predictivity in quantum gravity. In the first part, the concept of an asymptotically safe fixed point
is discussed within the functional Renormalization Group framework for gravity, which is also briefly reviewed. A concise overview of key results on asymptotically safe gravity is followed by a short discussion of important open questions. The second part highlights how the interplay with matter provides observational consistency tests for all quantum-gravity models, followed by an overview of the state of results on asymptotic safety and its implications in gravity-matter models. Finally, effective asymptotic safety is briefly discussed as a scenario in which asymptotically safe gravity could be connected to other approaches to quantum gravity.
