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Universe
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Asymptotic Safety in Quantum Gravity
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Asymptotic Safety in Quantum Gravity

A special issue of Universe (ISSN 2218-1997). This special issue belongs to the section "Foundations of Quantum Mechanics and Quantum Gravity".

Deadline for manuscript submissions: closed (30 June 2021) | Viewed by 20905

Special Issue Editor

Dr. Antonio Pereira

E-Mail Website
Guest Editor
Instituto de Física, Universidade Federal Fluminense
Interests: Renormalization Group; Quantum Gravity; Asymptotic Safety; Tensor Models; Group Field Theories; Continuum Limit; Non-Perturbative Effects

Special Issue Information

Dear Colleagues,

Elementary particles are described by fields which fluctuate quantum mechanically. The successful standard model of particle physics provides a consistent (albeit incomplete) description of the quantum theory for three of the four fundamental interactions of nature. Gravity is the vacillating force which resists the standard perturbative quantum-field-theoretic methods. Its classical description through general relativity has passed many non-trivial tests, including the very recent detection of gravitational waves and black hole shadows. However, according to our knowledge of quantum mechanics, there is no reason to expect that spacetime itself should not fluctuate quantum mechanically. Therefore, “quantum matter deforms quantum spacetime and quantum spacetime tells how quantum matter should move”. The application of standard perturbative methods to general relativity leads to a theory which is not valid up to arbitrarily large energy scales, leading to an effective field theory. Such a theory leads to predictions for quantum corrections of the classical general relativistic theory up to some ultraviolet cutoff, but it is not complete. Fundamentally, it must be replaced by a theory of quantum gravity. The asymptotic safety program is an approach to quantum gravity anchored in the successful quantum-field-theoretic technology. From this perspective, it is investigated if the quantum theory for the metric features an ultraviolet fixed point in the renormalization group flow. This represents a scale-invariant regime where all the couplings attain constant values. Such a mechanism prevents the generation of divergences and ensures that the theory is well defined up to arbitrarily short distances. This idea was put forward by Weinberg in the 1970s and became a systematic research area after the seminal work by Martin Reuter where functional renormalization tools were adapted to quantum gravity. There is now compelling evidence for the existence of such a scale-invariant regime, and the asymptotic safety program has become a mature and well-grounded approach to quantum gravity. Born from the tool of continuum quantum field theory, asymptotically safe quantum gravity can easily be coupled to the standard model of particle physics, and many exciting results have recently been obtained in this direction.

The purpose of this Special Issue is twofold: On the one hand, we aim to collect the state-of-the-art of this approach, clarifying the challenges to be faced in the coming years; on the other hand, this will be a place to show exciting new results in  the field, from formal aspects within this approach as well as phenomenological consequences of the existence of such a fixed point.

Submissions from related topics and approaches are very welcome.

Dr. Antonio Pereira
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Universe is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (10 papers)

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Editorial

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3 pages, 152 KiB  
Editorial
Editorial for the Special Issue “Asymptotic Safety in Quantum Gravity”
by Antonio D. Pereira
Universe 2022, 8(4), 198; https://0-doi-org.brum.beds.ac.uk/10.3390/universe8040198 - 23 Mar 2022
Viewed by 1292
Abstract
Asymptotically safe quantum gravity (ASQG) attempts to provide a standard quantum-field theoretic description of quantum spacetime across arbitrarily small length scales [...] Full article
(This article belongs to the Special Issue Asymptotic Safety in Quantum Gravity)

Research

Jump to: Editorial

23 pages, 37717 KiB  
Article
Asymptotic Safety: Swampland or Wonderland?
by Ivano Basile and Alessia Platania
Universe 2021, 7(10), 389; https://0-doi-org.brum.beds.ac.uk/10.3390/universe7100389 - 18 Oct 2021
Cited by 23 | Viewed by 1826
Abstract
We investigate the consequences of combining swampland conjectures with the requirement of asymptotic safety. To this end, we explore the infrared regime of asymptotically safe gravity in the quadratic one-loop approximation, and we identify the hypersurface spanned by the endpoints of asymptotically safe [...] Read more.
We investigate the consequences of combining swampland conjectures with the requirement of asymptotic safety. To this end, we explore the infrared regime of asymptotically safe gravity in the quadratic one-loop approximation, and we identify the hypersurface spanned by the endpoints of asymptotically safe renormalization group trajectories. These comprise the allowed values of higher-derivative couplings, as well as standard logarithmic form factors. We determine the intersection of this hypersurface with the regions of parameter space allowed by the weak-gravity conjecture, the swampland de Sitter conjecture, and the trans-Planckian censorship conjecture. The latter two depend on some order-one constants, for generic values of which we show that the overlap region is a proper subspace of the asymptotically safe hypersurface. Moreover, the latter lies inside the region allowed by the weak gravity conjecture assuming electromagnetic duality. Our results suggest a non-trivial interplay between the consistency conditions stemming from ultraviolet completeness of the renormalization group flow, black hole physics, and cosmology. Full article
(This article belongs to the Special Issue Asymptotic Safety in Quantum Gravity)
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45 pages, 3898 KiB  
Article
Asymptotically Safe Gravity-Fermion Systems on Curved Backgrounds
by Jesse Daas, Wouter Oosters, Frank Saueressig and Jian Wang
Universe 2021, 7(8), 306; https://0-doi-org.brum.beds.ac.uk/10.3390/universe7080306 - 19 Aug 2021
Cited by 18 | Viewed by 1808
Abstract
We set up a consistent background field formalism for studying the renormalization group (RG) flow of gravity coupled to Nf Dirac fermions on maximally symmetric backgrounds. Based on Wetterich’s equation, we perform a detailed study of the resulting fixed point structure in [...] Read more.
We set up a consistent background field formalism for studying the renormalization group (RG) flow of gravity coupled to Nf Dirac fermions on maximally symmetric backgrounds. Based on Wetterich’s equation, we perform a detailed study of the resulting fixed point structure in a projection including the Einstein–Hilbert action, the fermion anomalous dimension, and a specific coupling of the fermion bilinears to the spacetime curvature. The latter constitutes a mass-type term that breaks chiral symmetry explicitly. Our analysis identified two infinite families of interacting RG fixed points, which are viable candidates to provide a high-energy completion through the asymptotic safety mechanism. The fixed points exist for all values of Nf outside of a small window situated at low values Nf and become weakly coupled in the large Nf-limit. Symmetry-wise, they correspond to “quasi-chiral” and “non-chiral” fixed points. The former come with enhanced predictive power, fixing one of the couplings via the asymptotic safety condition. Moreover, the interplay of the fixed points allows for cross-overs from the non-chiral to the chiral fixed point, giving a dynamical mechanism for restoring the symmetry approximately at intermediate scales. Our discussion of chiral symmetry breaking effects provides strong indications that the topology of spacetime plays a crucial role when analyzing whether quantum gravity admits light chiral fermions. Full article
(This article belongs to the Special Issue Asymptotic Safety in Quantum Gravity)
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30 pages, 469 KiB  
Article
Essential Quantum Einstein Gravity
by Alessio Baldazzi and Kevin Falls
Universe 2021, 7(8), 294; https://0-doi-org.brum.beds.ac.uk/10.3390/universe7080294 - 10 Aug 2021
Cited by 34 | Viewed by 2208
Abstract
The non-perturbative renormalisation of quantum gravity is investigated allowing for the metric to be reparameterised along the RG flow, such that only the essential couplings constants are renormalised. This allows us to identify a universality class of quantum gravity which is guaranteed to [...] Read more.
The non-perturbative renormalisation of quantum gravity is investigated allowing for the metric to be reparameterised along the RG flow, such that only the essential couplings constants are renormalised. This allows us to identify a universality class of quantum gravity which is guaranteed to be unitary, since the physical degrees of freedom are those of general relativity without matter and with a vanishing cosmological constant. Considering all diffeomorphism invariant operators with up to four derivatives, only Newton’s constant is essential at the Gaussian infrared fixed point associated to the linearised Einstein–Hilbert action. The other inessential couplings can then be fixed to the values they take at the Gaussian fixed point along the RG flow within this universality class. In the ultraviolet, the corresponding beta function for Newton’s constant vanishes at the interacting Reuter fixed point. The properties of the Reuter fixed point are stable between the Einstein–Hilbert approximation and the approximation including all diffeomorphism invariant four derivative terms in the flow equation. Our results suggest that Newton’s constant is the only relevant essential coupling at the Reuter fixed point. Therefore, we conjecture that quantum Einstein gravity, the ultraviolet completion of Einstein’s theory of general relativity in the asymptotic safety scenario, has no free parameters in the absence of matter and in particular predicts a vanishing cosmological constant. Full article
(This article belongs to the Special Issue Asymptotic Safety in Quantum Gravity)
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10 pages, 301 KiB  
Article
Ellis–Bronnikov Wormholes in Asymptotically Safe Gravity
by G. Alencar, V. B. Bezerra, C. R. Muniz and H. S. Vieira
Universe 2021, 7(7), 238; https://0-doi-org.brum.beds.ac.uk/10.3390/universe7070238 - 10 Jul 2021
Cited by 13 | Viewed by 1681
Abstract
In this paper, we investigate the simplest wormhole solution—the Ellis–Bronnikov one—in the context of the asymptotically safe gravity (ASG) at the Planck scale. We work with three models, which employ the Ricci scalar, Kretschmann scalar, and squared Ricci tensor to improve the field [...] Read more.
In this paper, we investigate the simplest wormhole solution—the Ellis–Bronnikov one—in the context of the asymptotically safe gravity (ASG) at the Planck scale. We work with three models, which employ the Ricci scalar, Kretschmann scalar, and squared Ricci tensor to improve the field equations by turning the Newton constant into a running coupling constant. For all the cases, we check the radial energy conditions of the wormhole solution and compare them with those that are valid in general relativity (GR). We verified that asymptotic safety guarantees that the Ellis–Bronnikov wormhole can satisfy the radial energy conditions at the throat radius, r0, within an interval of values of the latter, which is quite different from the result found in GR. Following this, we evaluate the effective radial state parameter, ω(r), at r0, showing that the quantum gravitational effects modify Einstein’s field equations in such a way that it is necessary to have a very exotic source of matter to generate the wormhole spacetime–phantom or quintessence-like matter. This occurs within some ranges of the throat radii, even though the energy conditions are or are not violated there. Finally, we find that, although at r0 we have a quintessence-like matter, upon growing r, we inevitably came across phantom-like regions. We speculate whether such a phantom fluid must always be present in wormholes in the ASG context or even in more general quantum gravity scenarios. Full article
(This article belongs to the Special Issue Asymptotic Safety in Quantum Gravity)
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36 pages, 683 KiB  
Article
Non-Perturbative Propagators in Quantum Gravity
by Benjamin Knorr and Marc Schiffer
Universe 2021, 7(7), 216; https://0-doi-org.brum.beds.ac.uk/10.3390/universe7070216 - 29 Jun 2021
Cited by 32 | Viewed by 1754
Abstract
We employ non-perturbative renormalisation group methods to compute the full momentum dependence of propagators in quantum gravity in general dimensions. We disentangle all different graviton and Faddeev–Popov ghost modes and find qualitative differences in the momentum dependence of their propagators. This allows us [...] Read more.
We employ non-perturbative renormalisation group methods to compute the full momentum dependence of propagators in quantum gravity in general dimensions. We disentangle all different graviton and Faddeev–Popov ghost modes and find qualitative differences in the momentum dependence of their propagators. This allows us to reconstruct the form factors that are quadratic in curvature from first principles, which enter physical observables like scattering cross sections. The results are qualitatively stable under variations of the gauge fixing choice. Full article
(This article belongs to the Special Issue Asymptotic Safety in Quantum Gravity)
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18 pages, 376 KiB  
Article
The Search for the Universality Class of Metric Quantum Gravity
by Riccardo Martini, Alessandro Ugolotti and Omar Zanusso
Universe 2021, 7(6), 162; https://0-doi-org.brum.beds.ac.uk/10.3390/universe7060162 - 26 May 2021
Cited by 10 | Viewed by 2068
Abstract
On the basis of a limited number of reasonable axioms, we discuss the classification of all the possible universality classes of diffeomorphisms invariant metric theories of quantum gravity. We use the language of the renormalization group and adopt several ideas which originate in [...] Read more.
On the basis of a limited number of reasonable axioms, we discuss the classification of all the possible universality classes of diffeomorphisms invariant metric theories of quantum gravity. We use the language of the renormalization group and adopt several ideas which originate in the context of statistical mechanics and quantum field theory. Our discussion leads to several ideas that could affect the status of the asymptotic safety conjecture of quantum gravity and give universal arguments towards its proof. Full article
(This article belongs to the Special Issue Asymptotic Safety in Quantum Gravity)
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21 pages, 575 KiB  
Article
Towards a Geometrization of Renormalization Group Histories in Asymptotic Safety
by Renata Ferrero and Martin Reuter
Universe 2021, 7(5), 125; https://0-doi-org.brum.beds.ac.uk/10.3390/universe7050125 - 01 May 2021
Cited by 4 | Viewed by 1428
Abstract
Considering the scale-dependent effective spacetimes implied by the functional renormalization group in d-dimensional quantum Einstein gravity, we discuss the representation of entire evolution histories by means of a single, (d+1)-dimensional manifold furnished with a fixed (pseudo-) Riemannian structure. [...] Read more.
Considering the scale-dependent effective spacetimes implied by the functional renormalization group in d-dimensional quantum Einstein gravity, we discuss the representation of entire evolution histories by means of a single, (d+1)-dimensional manifold furnished with a fixed (pseudo-) Riemannian structure. This “scale-spacetime” carries a natural foliation whose leaves are the ordinary spacetimes seen at a given resolution. We propose a universal form of the higher dimensional metric and discuss its properties. We show that, under precise conditions, this metric is always Ricci flat and admits a homothetic Killing vector field; if the evolving spacetimes are maximally symmetric, their (d+1)-dimensional representative has a vanishing Riemann tensor even. The non-degeneracy of the higher dimensional metric that “geometrizes” a given RG trajectory is linked to a monotonicity requirement for the running of the cosmological constant, which we test in the case of asymptotic safety. Full article
(This article belongs to the Special Issue Asymptotic Safety in Quantum Gravity)
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20 pages, 17482 KiB  
Article
Towards Black-Hole Singularity-Resolution in the Lorentzian Gravitational Path Integral
by Johanna N. Borissova and Astrid Eichhorn
Universe 2021, 7(3), 48; https://0-doi-org.brum.beds.ac.uk/10.3390/universe7030048 - 27 Feb 2021
Cited by 26 | Viewed by 1969
Abstract
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 black-hole singularities both in the spherically symmetric and axisymmetric case. [...] Read more.
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 black-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. Full article
(This article belongs to the Special Issue Asymptotic Safety in Quantum Gravity)
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76 pages, 1379 KiB  
Article
Effective Scalar Potential in Asymptotically Safe Quantum Gravity
by Christof Wetterich
Universe 2021, 7(2), 45; https://0-doi-org.brum.beds.ac.uk/10.3390/universe7020045 - 17 Feb 2021
Cited by 19 | Viewed by 2107
Abstract
We compute the effective potential for scalar fields in asymptotically safe quantum gravity. A scaling potential and other scaling functions generalize the fixed point values of renormalizable couplings. The scaling potential takes a non-polynomial form, approaching typically a constant for large values of [...] Read more.
We compute the effective potential for scalar fields in asymptotically safe quantum gravity. A scaling potential and other scaling functions generalize the fixed point values of renormalizable couplings. The scaling potential takes a non-polynomial form, approaching typically a constant for large values of scalar fields. Spontaneous symmetry breaking may be induced by non-vanishing gauge couplings. We strengthen the arguments for a prediction of the ratio between the masses of the top quark and the Higgs boson. Higgs inflation in the standard model is unlikely to be compatible with asymptotic safety. Scaling solutions with vanishing relevant parameters can be sufficient for a realistic description of particle physics and cosmology, leading to an asymptotically vanishing “cosmological constant” or dynamical dark energy. Full article
(This article belongs to the Special Issue Asymptotic Safety in Quantum Gravity)
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