Asymptotic solutions in asymptotic safety

González-Martín, Sergio; Morris, Tim R.; Slade, Zoë H.

doi:10.1103/physrevd.95.106010

Cited by 50 publications

(49 citation statements)

References 51 publications

(163 reference statements)

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“…We observe that in the full solution and in the µ * eff (r) = µ * 0 approximation there are no solutions to the background EoM within the investigated curvature regime. This absence of a constant curvature solution is in agreement with studies of f (R) gravity in the background field approximation [116], although solutions have been found in calculations exploiting the exponential parameterisation [118,119] and within the geometrical approach [43,49]. For the approximation µ * (r) = µ * 0 , which corresponds to a pure Einstein-Hilbert computation, we find a minimum at r 0 = 0.97.…”

Section: B Background Potentialsupporting

confidence: 89%

Curvature dependence of quantum gravity

et al. 2018

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We investigate the phase diagram of quantum gravity with a vertex expansion about constantlycurved backgrounds. The graviton two-and three-point function are evaluated with a spectral sum on a sphere. We obtain, for the first time, curvature-dependent UV fixed point functions of the dynamical fluctuation couplings g * (R), µ * (R), and λ * 3 (R), and the background f (R)-potential. Based on these fixed point functions we compute solutions to the quantum and the background equation of motion with and without Standard Model matter. We have checked that the solutions are robust against changes of the truncation.

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Section: B Background Potentialsupporting

confidence: 89%

Curvature dependence of quantum gravity

et al. 2018

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“…Note that with a rescaling of our unique cutoff scale in Sec. VI with N 2 c we already arrive at the N c independent fixed point values (62). The large values come from dropping the N c -independent prefactor in the ratio G=G eff .…”

Section: Uv Dominance Of Gravity a Dynamical Scale Fixingmentioning

confidence: 73%

“…and vanish in the large N c scaling of (62). It is simple to show that the further diagrams in the fixed point equations of w 2 , v 2 proportional to w 2 , v 2 decay even faster when using (67) for the diagrams.…”

Section: Decoupling Of Gravity-induced Gluon Self-interactionsmentioning

confidence: 99%

Asymptotic safety of gravity with matter

et al. 2018

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We study the asymptotic safety conjecture for quantum gravity in the presence of matter fields. A general line of reasoning is put forward explaining why gravitons dominate the high-energy behavior, largely independently of the matter fields as long as these remain sufficiently weakly coupled. Our considerations are put to work for gravity coupled to Yang-Mills theories with the help of the functional renormalization group. In an expansion about flat backgrounds, explicit results for beta functions, fixed points, universal exponents, and scaling solutions are given in systematic approximations exploiting running propagators, vertices, and background couplings. Invariably, we find that the gauge coupling becomes asymptotically free while the gravitational sector becomes asymptotically safe. The dependence on matter field multiplicities is weak. We also explain how the scheme dependence, which is more pronounced, can be handled without changing the physics. Our findings offer a new interpretation of many earlier results, which is explained in detail. The results generalize to theories with minimally coupled scalar and fermionic matter. Some implications for the ultraviolet closure of the Standard Model or its extensions are given.

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“…(3) While it is straightforward to solve the RG equations numerically, there exists a conve- 5 We refer the reader to [23][24][25][26][27][28] for a partial list of recent results. nient analytical approximation for Type IIIa trajectories which leads to transparent closedform results often.…”

Section: The Einstein-hilbert Examplementioning

confidence: 99%

Background independent quantum field theory and gravitating vacuum fluctuations

Pagani

Reuter

2019

Annals of Physics

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The scale dependent effective average action for quantum gravity complies with the fundamental principle of Background Independence. Ultimately the background metric it formally depends on is selected self-consistently by means of a tadpole condition, a generalization of Einstein's equation. Self-consistent backround spacetimes are scale dependent, and therefore "going on-shell" at the points along a given renormalization group (RG) trajectory requires understanding two types of scale dependencies: the (familiar) direct one carried by the off-shell action functional, and an equally important indirect one related to the continual re-adjustment of the background geometry. This paper is devoted to a careful delineation and analysis of certain general questions concerning the indirect scale dependence, as well as a detailed explicit investigation of the case where the self-consistent metrics are determined predominantly by the RG running of the cosmological constant. Mathematically, the object of interest is the spectral flow induced by the background Laplacian which, on-shell, acquires an explicit scale dependence. Among other things, it encodes the complete information about the specific set of field modes which, at any given scale, are the degrees of freedom constituting the respective effective field theory. For a large class of RG trajectories (Type IIIa) we discover a seemingly paradoxical behavior that differs substantially from the off-shell based expectations: A Background Independent theory of (matter coupled) quantum gravity looses rather than gains degrees of freedom at increasing energies. As an application, we investigate to what extent it is possible to reformulate the exact theory in terms of matter and gravity fluctuations on a rigid flat space. It turns out that, in vacuo, this "rigid picture" breaks down after a very short RG time already (less than one decade of scales) because of a "scale horizon" that forms. Furthermore, we critically reanalyze, and refute the frequent claim that the huge energy densities one obtains in standard quantum field theory by summing up to zero-point energies imply a naturalness problem for the observed small value of the cosmological constant. arXiv:1906.02507v1 [gr-qc] 6 Jun 2019 1 Writing the dimensionless ratio Λ/m 2 Pl and the energy density ρ Λ ≡ Λ/ (8πG), with m Pl ≡ G −1/2 , in the style Λ/m 2 Pl = ΛG = Ω Λ h 2 ×9.15·10 −122 and ρ Λ = Ω 1/4 Λ h 1/2 × 3.0 meV 4 , the recently measured Ω Λ ≈ 0.68, h ≈ 0.67 yield the observational values Λ/m 2 Pl ≈ 2.8 · 10 −122 and ρ Λ = [2.2 meV] 4 , respectively [5].

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Asymptotic solutions in asymptotic safety

Cited by 50 publications

References 51 publications

Curvature dependence of quantum gravity

Curvature dependence of quantum gravity

Asymptotic safety of gravity with matter

Background independent quantum field theory and gravitating vacuum fluctuations

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