Editorial for the Special Issue “Asymptotic Safety in Quantum Gravity”

Asymptotically safe quantum gravity (ASQG) attempts to provide a standard quantum-field theoretic description of quantum spacetime across arbitrarily small length scales. Asymptotic safety is a generalization of asymptotic freedom, meaning that the coupling constants of the underlying quantum field theory (QFT) feature an interacting fixed point along their renormalization group (RG) flow. At such a fixed point, the theory displays (quantum) scale symmetry and the dimensionless versions of the coupling constants are finite. As such, the ultraviolet cutoffs introduced to regularize the theory can be safely removed and the resulting QFT will be valid at arbitrarily large energy scales and thereby correspond to a fundamental theory (in contrast to an effective description). In the last two decades, a robust body of evidence has been collected regarding the existence of such a non-trivial fixed point. Since it interacts, the fixed point might not be probed by perturbative techniques, and it is necessary to use non-perturbative tools. Such a computational challenge has been tackled, within the continuum of the QFT realm, mostly by the functional renormalization group. Pure gravity systems have been analyzed within sophisticated approximations to determine their quantum dynamics, and compelling evidence of the existence of a predictive interacting fixed point has been seen. Formulated as a “standard” continuum QFT, ASQG is friendly to the inclusion of matter degrees of freedom. Investigating gravity–matter systems is essential for the verification of the consistency of this approach to quantum gravity. After all, quantum fluctuations in matter can destroy the quantum-scale symmetric regime in ASQG. Thus, establishing whether the matter content of the standard model of particle physics (along with its potential phenomenological extensions) is compatible with the existence of a non-trivial fixed point for the gravity–matter system is central to the asymptotic safety program. Finally, by postulating the validity of the ASQG proposal, one can derive its potential consequences in effective cosmological scenarios, black-hole physics, and other astrophysical objects which might hint at potential tests of quantum-gravity signatures in the sky. This Special Issue provides a collection of works which touch upon those various aspects of ASQG. These works range from articles describing technical developments which significantly increase the sophistication of the calculations performed with the functional renormalization group and thereby substantially enhance our understanding of the fixed-point structure to articles focusing on the phenomenological implications of the asymptotic safety paradigm. In the following, we provide a short summary of the contributions to this Special Issue.

In [1], a thorough investigation of the effects of quantum gravity on the effective potential of scalar fields is provided. In particular, besides the technical developments made regarding the scaling behavior of the scalar potential, this paper highlights the phenomenological consequences of the interplay between quantum gravity and scalar fields degrees of freedom, ranging from the prediction of the Higgs mass to dynamical dark energy.

It is often expected that a consistent theory of quantum gravity will resolve spacetime singularities. In [2], the authors explore the impact of such a requirement on the Lorentzian path integral of quantum gravity. Remarkably, different choices regarding the microscopic action in the path integral lead to different dynamical fates of singular solutions. Hence, this constitutes a promising avenue by which to search for the fundamental action present in the path integral of quantum gravity, which is a crucial piece of information for the asymptotic safety scenario.

The asymptotic safety program is underpinned by the structure of the renormalization group in QFT. The contribution [3] introduces a geometrical framework for the renormalization group and embeds the RG scale as an extra dimension. This is carried out in harmony with the functional renormalization group and applied in the case of ASQG. In particular, relations between the geometrized RG structures and the flow of gravitational couplings, such as the cosmological constant, are established.

The existence of a non-trivial fixed point that allows for a well-defined continuum limit in quantum gravity can define a universality class which could be probed by different methods. Characterizing such a universality class is fundamental in order to bring together complementary techniques that could probe such a non-perturbative continuum limit. In [4], the authors propose a set of criteria for the establishment of such universality classes of metric theories which are diffeomorphism invariant.

Functional renormalization group flows are driven by dressed correlation functions and thus encode non-perturbative information. Notably, the propagators of elementary fields are the most fundamental correlators, and a deep understanding of their structure can reveal the essential properties of the underlying theory. The contribution [5] describes a remarkable step forward in the characterization of the full momentum dependence of the graviton and Faddeev–Popov ghost propagators in their different irreducible sectors. This enables the reconstruction of some of the building blocks of physical quantities from a first-principle lens.

The scale dependence of the Newton constant within ASQG is explored in [6], with a particular focus on wormhole solutions. The authors explore different renormalization-group improvements of the Ellis–Bronnikov wormhole solution and thereby how quantum gravity-inspired effects impact the classical counterpart.

In [7], the authors provide a different perspective of the asymptotic safety program, implementing a renormalization group flow that, thanks to appropriate field reparameterizations, renormalize just the essential couplings of the theory. Such a framework provides a clear control of the degrees of freedom of the theory and removes the unphysical artifacts that are often considered in the standard renormalization group scheme, thereby constituting a potential key ingredient in the characterization of the universality class of (asymptotically safe) quantum gravity.

As previously mentioned, in order to define a fundamental theory that can describe our universe, the asymptotic safety scenario must also be able to accommodate matter degrees of freedom. In [8], the authors provide a systematic investigation of gravity-fermion systems. Besides finding evidence for asymptotically safe fixed points, they provide a detailed analysis of the interplay between spacetime topology and chiral symmetry. Ultimately, since physics should not be affected by different choices of the background metric and due to our phenomenological constraints on chiral symmetry breaking, this work provides a very interesting concrete example of how quantum spacetime can constrain quantum matter and vice versa in the asymptotic safety program.

The contribution [9] brings together the asymptotic safety paradigm and the swampland conjectures originally introduced in the context of string theory. In particular, the infrared regime of ASQG is constrained by swampland conjectures. This work constitutes an explicit example of how such conjectures can be applied in a broader quantum gravitational context and contributes to a possible link between asymptotic safety and string theory.

With these contributions, the present Special Issue covers many different facets of ASQG, ranging from its foundations to its phenomenological applications. The field still has many open questions that need to be addressed, but it has definitely matured at both the conceptual and computational levels over the last two decades, and substantial progress is expected to be seen in the upcoming years.