Aspects of asymptotic safety for quantum gravity

Falls, Kevin; Litim, Daniel F.; Schröder, Jan

doi:10.1103/physrevd.99.126015

Cited by 117 publications

(144 citation statements)

References 135 publications

(310 reference statements)

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“…This UV fixed point would make the theory UV finite and thus non-perturbatively renormalizable. Starting with the seminal work by Reuter [15], a lot of evidence was collected in favour of this scenario [16][17][18][19][20][21][22][23][24][25][26][27][28][29]. The interplay of quantum gravity and matter was extensively investigated as well [30][31][32][33][34][35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Dark matter meets quantum gravity

Reichert

Smirnov

2020

Phys. Rev. D

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We search for an extension of the Standard Model that contains a viable dark matter candidate and that can be embedded into a fundamental, asymptotically safe, quantum field theory with quantum gravity. Demanding asymptotic safety leads to boundary conditions for the non-gravitational couplings at the Planck scale. For a given dark matter model these translate into constraints on the mass of the dark matter candidate. We derive constraints on the dark matter mass and couplings in two minimal dark matter models: i) scalar dark matter coupled via the Higgs-portal in the B-L model; ii) fermionic dark matter in a U (1)X extension of the Standard Model, coupled via the new gauge boson. For scalar dark matter we find 56 GeV < MDM < 63 GeV, and for fermionic dark matter MDM ≤ 37 TeV. Within our framework, we identify three benchmark scenarios with distinct phenomenological consequences.

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Section: Introductionmentioning

confidence: 99%

Dark matter meets quantum gravity

Reichert

Smirnov

2020

Phys. Rev. D

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“…At least in the matrix-model case, multi-trace interac- tions actually encode higher-order curvature terms, see, e.g., [100,101]. Results in continuum studies of asymptotically safe gravity suggest that higher-order curvature terms are relevant, see, e.g., [70,72,73,[102][103][104][105][106][107]. We therefore tentatively suggest that including multitrace interactions might be important to escape the branched polymer phase.…”

Section: Interacting Fixed Pointmentioning

confidence: 78%

Universal critical behavior in tensor models for four-dimensional quantum gravity

Eichhorn

Lumma

Pereira

et al. 2020

J. High Energ. Phys.

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Four-dimensional random geometries can be generated by statistical models with rank-4 tensors as random variables. These are dual to discrete building blocks of random geometries. We discover a potential candidate for a continuum limit in such a model by employing background-independent coarse-graining techniques where the tensor size serves as a pre-geometric notion of scale. A fixed point candidate which features two relevant directions is found. The possible relevance of this result in view of universal results for quantum gravity and a potential connection to the asymptotic-safety program is discussed. I. THE CASE FOR UNIVERSAL, BACKGROUND-INDEPENDENT QUANTUM GRAVITYTo describe physically relevant spacetimes, such as black holes or Friedmann-Lemaitre-Robertson-Walker spacetimes, it is necessary to go beyond General Relativity, where these spacetimes feature singularities. Such singularities are expected to be resolved once quantum fluctuations of spacetime are properly accounted for. Yet, this is a particularly challenging task if it is to be compatible with the background-independence at the heart of our modern understanding of gravity. Backgroundindependence implies that no configuration of spacetime should be singled out a priori from all configurations that enter the path integral. This is incompatible with perturbative techniques around a fixed spacetime, which single out a special background to perturb around, and which do not provide a predictive quantum field theory of gravity. Instead, one is led to introduce an infinite number of independent local counterterms to cancel divergences at each loop order [1][2][3]. This motivates that background independence should be taken seriously in the search for an ultraviolet complete definition of the gravitational path integral. Thus, we aim at an implementation of the path integral without auxiliary geometric background structures 1 . A promising route to construct a background independent path integral consists of making a transition to discrete building blocks, as in dynamical triangulations [5], Regge calculus [6], matrix/tensor models [7-9], spin foams [10] and causal sets [11]. This allows to construct a discrete approximation of all random geometries (and potentially additional configurations with no interpreta- * eichhorn@cp3.sdu.dk † j.lumma@thphys.uni-heidelberg.de ‡ adpjunior@id.uff.br § a.sikandar@thphys.uni-heidelberg.de 1 An alternative route makes use of an auxiliary background structure at the technical level while ensuring the independence of physical results from this background structure, see, e.g., [4].tion as a spacetime geometry) that enter the path integral for quantum gravity. These discrete building blocks are typically not viewed as physical, "fundamental" building blocks of spacetime. Rather, they are auxiliary, unphysical entities, allowing to define a regularized path integral in analogy to lattice gauge theories for non-gravitational quantum field theories. One might object that quantum spacetime might be fundamentally discrete, wh...

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“…At this stage, it is instructive to compare the results (3.14) to the ones obtained from solving the Wetterich equation (2.1) projected onto gravitational actions of f (R)-type [31,32,51]. Performing a polynomial expansion of f (R) N n=0ū n R n , the eigenvalues of the stability matrix (2.5) have been determined for successively increasing values N = 6 [31,32], N = 8 [121], N = 35 [40,41], and lately also N = 71 [113]. Building on previous investigations [40,41], ref.…”

Section: Comparison To the Polynomial F (R)-truncationmentioning

confidence: 99%

“…Building on previous investigations [40,41], ref. [113] reported that for large values of n the real parts of the eigenvalues λ n follow an almost Gaussian behavior λ f (R) n ≈ a n − b , (3.17) where the best-fit values for the parameters a and b are a = 2.042 ± 0.002 , b = 2.91 ± 0.05 . (3.18) In order to connect the results (3.17) and (3.14) we follow the strategy outlined in [25].…”

Section: Comparison To the Polynomial F (R)-truncationmentioning

confidence: 99%

On the scaling of composite operators in asymptotic safety

Houthoff

Kurov

Saueressig

2020

J. High Energ. Phys.

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The Asymptotic Safety hypothesis states that the high-energy completion of gravity is provided by an interacting renormalization group fixed point. This implies nontrivial quantum corrections to the scaling dimensions of operators and correlation functions which are characteristic for the corresponding universality class. We use the composite operator formalism for the effective average action to derive an analytic expression for the scaling dimension of an infinite family of geometric operators d d x √ gR n . We demonstrate that the anomalous dimensions interpolate continuously between their fixed point value and zero when evaluated along renormalization group trajectories approximating classical general relativity at low energy. Thus classical geometry emerges when quantum fluctuations are integrated out. We also compare our results to the stability properties of the interacting renormalization group fixed point projected to f (R)-gravity, showing that the composite operator formalism in the single-operator approximation cannot be used to reliably determine the number of relevant parameters of the theory.

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Aspects of asymptotic safety for quantum gravity

Cited by 117 publications

References 135 publications

Dark matter meets quantum gravity

Dark matter meets quantum gravity

Universal critical behavior in tensor models for four-dimensional quantum gravity

On the scaling of composite operators in asymptotic safety

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