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The Asymptotic Safety Paradigm for Quantum Spacetime and Matter

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The Asymptotic Safety Paradigm for Quantum Spacetime and Matter The asymptotic safety paradigm for quantum spacetime and matter Workshop on gravitational waves, black holes and spacetime singularities Vatican Observatory May 2017 Astrid Eichhorn University of Heidelberg The asymptotic safety paradigm for quantum spacetime and matter Workshop on gravitational waves, black holes and spacetime singularities Vatican Observatory A. Platania: May 2017 !Cosmic censorship in QEG F. Saueressig: !Cosmic perturbations from Astrid Eichhorn Asymptotic Safety University of Heidelberg Starting point: Singularities • Incompleteness of General Relativity • Incompleteness of the Standard Model of particle physics e2 k H L k Starting point: Singularities • Incompleteness of General Relativity • Incompleteness of the Standard Model of particle physics e2 k H L k Fundamental description of spacetime needs QFT ! and QFTs of matter need gravity Starting point: Singularities • Incompleteness of General Relativity • Incompleteness of the Standard Model of particle physics iS[gµ⌫ ,φ] goal: gµ⌫ φStandard Modele ! D D Z Starting point: Singularities • Incompleteness of General Relativity • Incompleteness of the Standard Model of particle physics e2 k iS[gµ⌫ ,φ] goal: gµ⌫ φStandard Modele ! D D H L Z quantum fluctuations k scale dependent (running) couplings ) example: Quantum Electrodynamics 1/k + quantum vacuum = screening medium { e (k) Starting point: Singularities • Incompleteness of General Relativity • Incompleteness of the Standard Model of particle physics e2 k iS[gµ⌫ ,φ] goal: gµ⌫ φStandard Modele ! D D H L Z quantum fluctuations k scale dependent (running) couplings ) example: Quantum Electrodynamics 1/k + quantum vacuum = screening medium { e (k) qm fluc’s of metric: scale dependent grav. coupling ) High-energy behavior in QFTs running coupling asymptotically: in QCD: scale-invariance Asymptotic freedom without interactions CMS ‘14 [Gross, Wilczek; Politzer ’73] High-energy behavior in QFTs running coupling asymptotically: in QCD: scale-invariance Asymptotic freedom without interactions CMS ‘14 [Gross, Wilczek; Politzer ’73] 2 running coupling e k in QED: H L 1/k + Landau pole/triviality { e (k) new physics! [Gell-Mann, Low ’54; Gockeler et al. ’97; k Gies, Jaeckel ‘04] ⇤ High-energy behavior in QFTs running coupling asymptotically: in QCD: scale-invariance Asymptotic freedom without interactions CMS ‘14 [Gross, Wilczek; Politzer ’73] 2 running coupling e k in QED: H L 1/k + Landau pole/triviality { e (k) new physics! [Gell-Mann, Low ’54; Gockeler et al. ’97; k Gies, Jaeckel ‘04] ⇤ in Standard Model: U(1)hypercharge & Higgs quartic coupling affected High-energy behavior in QFTs running coupling asymptotically: in QCD: scale-invariance Asymptotic freedom without interactions CMS ‘14 [Gross, Wilczek; Politzer ’73] 2 running coupling e k in QED: H L 1/k + Landau pole/triviality { e (k) new physics! [Gell-Mann, Low ’54; Gockeler et al. ’97; k Gies, Jaeckel ‘04] ⇤ G[k] asymptotically: scale-invariance with interactions Asymptotic safety [Weinberg ’76] Log[k] High-energy behavior in QFTs running coupling asymptotically: in QCD: scale-invariance Asymptotic freedom without interactions CMS ‘14 [Gross, Wilczek; Politzer ’73] 2 running coupling e k in QED: H L 1/k + Landau pole/triviality { e (k) new physics! [Gell-Mann, Low ’54; Gockeler et al. ’97; k Gies, Jaeckel ‘04] ⇤ G[k] running coupling asymptotically: in gravity? scale-invariance with interactions Asymptotic safety [Weinberg ’76] Log[k] High-energy behavior in QFTs running coupling asymptotically: in QCD: scale-invariance Asymptotic freedom without interactions CMS ‘14 [Gross, Wilczek; Politzer ’73] 2 running coupling e k in QED: H L 1/k + Landau pole/triviality { e (k) new physics! [Gell-Mann, Low ’54; Gockeler et al. ’97; k Gies, Jaeckel ‘04] ⇤ G[k] running coupling Quantum-field theoreticasymptotically: description ) in gravity? of fundamental microscopicscale-invariance structure with interactions Asymptotic safety of spacetime [Weinberg ’76] Log[k] High-energy behavior in QFTs running coupling asymptotically: in QCD: scale-invariance Asymptotic freedom without interactions CMS ‘14 [Gross, Wilczek; Politzer ’73] qm fluc’s of gravity:e 2 k running coupling sizeable for E M Planck in QED: ⇡ H L 1/k + { cannot probe Landau pole/triviality ) e (k) running coupling new physics! [Gell-Mann, Low ’54; Gockeler et al. ’97; k Gies, Jaeckel ‘04] directly (yet?) ⇤ G[k] running coupling asymptotically: in gravity? scale-invariance with interactions Asymptotic safety [Weinberg ’76] Log[k] Functional Renormalization Group - zooming in on quantum spacetime Functional Renormalization Group - zooming in on quantum spacetime probe scale dependence of QFT UV scale-invariant regime S G[k] Γk contains effect of quantum fluctuations above k Log[k] Γk 0 ! classical regime Functional Renormalization Group - zooming in on quantum spacetime probe scale dependence of QFT Γ [φ] S['] 1 '( p)R (p)'(p) e− k = 'e− − 2 − k D R Z Wetterich ’93; Morris, ‘94 scale- and momentum- S dependent ``mass”: dials ``resolution scale” Γk contains effect of quantum fluctuations above k Γk 0 ! Functional Renormalization Group - zooming in on quantum spacetime probe scale dependence of QFT Γ [φ] S['] 1 '( p)R (p)'(p) e− k = 'e− − 2 − k D R Z Wetterich ’93; Morris, ‘94 scale- and momentum- S dependent ``mass”: dials ``resolution scale” Wetterich equation: contains effect of quantum 1 Γk 1 (2) − fluctuations above k @kΓk = STr Γ + Rk @kRk 2 k ⇣ ⌘ = Γk 0 ! Asymptotic safety for quantum gravity 1 4 ¯ 2 ¯ 2 Γ = d xpg (R 2λ(k)) G(k)=GN (k)k ,λ(k)=λ(k)/k k −16⇡G (k) − N Z 0.4 towards IR 0.3 0.2 G 0.1 0.0 -0.1 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 l Reuter, ’96; Reuter, Saueressig ‘01, Litim, ‘03 Asymptotic safety for quantum gravity 1 4 ¯ 2 ¯ 2 Γ = d xpg (R 2λ(k)) G(k)=GN (k)k ,λ(k)=λ(k)/k k −16⇡G (k) − N Z 0.4 towards IR UV scale-invariant regime 0.3 0.2 G 0.1 k@kG(k)=0 G[k] 0.0 -0.1 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 l Log[k] Reuter, ’96; Reuter, Saueressig ‘01, Litim, ‘03 Asymptotic safety for quantum gravity 1 4 ¯ 2 ¯ 2 Γ = d xpg (R 2λ(k)) G(k)=GN (k)k ,λ(k)=λ(k)/k k −16⇡G (k) − N Z 0.4 towards IR UV scale-invariant regime 0.3 0.2 G 0.1 k@kG(k)=0 G[k] classical regime 0.0 -0.1 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 l Log[k] Reuter, ’96; Reuter, Saueressig ‘01, Litim, ‘03 GN (k) = const Asymptotic safety for quantum gravity 1 4 ¯ 2 ¯ 2 Γ = d xpg (R 2λ(k)) G(k)=GN (k)k ,λ(k)=λ(k)/k k −16⇡G (k) − N Z 0.4 0.3 quantum fluctuations of metric 0.2 generate additional terms G in the microscopic dynamics 0.1 Γk =ΓEH 0.0 4 2 4 µ⌫ 4 +a d x pgR + b d x pgRµ⌫ R + c d x pgR⇤R + ... Z Z Z -0.1 finite number of free parameters (= predictivity) -0.1 0.0 0.1 0.2 0.3 0.4 0.5 finite number of UV attractive directions l ! A.S. predicts values of all other couplings Reuter, ’96; Reuter, Saueressig ‘01, Litim, ‘03 ) Asymptotic safety for quantum gravity 1 4 ¯ 2 ¯ 2 Γ = d xpg (R 2λ(k)) G(k)=GN (k)k ,λ(k)=λ(k)/k k −16⇡G (k) − N Z 0.4 extended tests: N Reuter, Lauscher, ’02; Codello, Percacci, Rahmede, ’09; n Benedetti, Caravelli, ’12; Dietz, Morris, ’12; f(R)= anR Falls, Litim, Nikolakopoulos, Rahmede, ’13, ‘14 0.3 n=0 Demmel, Saueressig, Zanusso, ’15; Eichhorn ‘15 X 2 µ⌫ Benedetti, Machado, Saueressig, ‘09 R ,Rµ⌫ R 0.2 Christiansen, ’16, Oda, Yamada ‘17 ⇢ µ⌫ G Cµ⌫ C C⇢ Gies, Knorr, Lippoldt, Saueressig ‘16 0.1 0.0 -0.1 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 l perturbative counterterms: asymptotic safety Reuter, ’96; Reuter, Saueressig ‘01, Litim, ‘03 ’t Hooft, Veltman ’74; Deser, Niewenhuizen ’74; Christensen, Duff ’80; Goroff, Sagnotti ’85, ’86; Van de Ven ‘92 Asymptotic safety for quantum gravity 1 4 ¯ 2 ¯ 2 Γ = d xpg (R 2λ(k)) G(k)=GN (k)k ,λ(k)=λ(k)/k k −16⇡G (k) − N Z 0.4 extended tests: N Reuter, Lauscher, ’02; Codello, Percacci, Rahmede, ’09; n Benedetti, Caravelli, ’12; Dietz, Morris, ’12; f(R)= anR Falls, Litim, Nikolakopoulos, Rahmede, ’13, ‘14 0.3 n=0 Demmel, Saueressig, Zanusso, ’15; Eichhorn ‘15 compelling hints X 2 µ⌫ Benedetti, Machado, Saueressig, ‘09 R ,Rµ⌫ R 0.2 for existence of Christiansen, ’16, Oda, Yamada ‘17 ⇢ µ⌫ G UV scale invariance Cµ⌫ C C⇢ Gies, Knorr, Lippoldt, Saueressig ‘16 0.1 in quantum gravity 0.0 -0.1 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 l perturbative counterterms: asymptotic safety Reuter, ’96; Reuter, Saueressig ‘01, Litim, ‘03 ’t Hooft, Veltman ’74; Deser, Niewenhuizen ’74; Christensen, Duff ’80; Goroff, Sagnotti ’85, ’86; Van de Ven ‘92 Asymptotic safety for quantum gravity 1 4 ¯ 2 ¯ 2 Γ = d xpg (R 2λ(k)) G(k)=GN (k)k ,λ(k)=λ(k)/k k −16⇡G (k) − N Z 0.4 0.3 quantum fluctuations of metric 0.2 generate additional terms G in the microscopic dynamics 0.1 Γk =ΓEH 0.0 4 2 4 µ⌫ 4 +a d x pgR + b d x pgRµ⌫ R + c d x pgR⇤R + ... Z Z Z -0.1 microscopic values = fixed-point values -0.1 0.0 0.1 0.2 0.3 0.4 0.5 l observational constraints ? ! (e.g. grav. waveforms) Reuter, ’96; Reuter, Saueressig ‘01, Litim, ‘03 Microscopic structure of spacetime: Hints for dimensional reduction to 2 Microscopic structure of spacetime: Hints for dimensional reduction to 2 Probe (Eucl.) spacetime by a fictitious diffusing particle: Microscopic structure of spacetime: Hints for dimensional reduction to 2 Probe (Eucl.) spacetime by a fictitious diffusing particle: classically: spectral dimension from return probability 2 @ P (x, x0,σ)=0 σ r Microscopic structure of spacetime: Hints for dimensional reduction to 2 Probe (Eucl.) spacetime by a fictitious diffusing particle: classically: spectral dimension from return probability 2 @ P (x, x0,σ)=0 σ r @lnP (x, x, σ) d = 2 =4 s − @lnσ Microscopic structure of spacetime: Hints for dimensional reduction to 2 Probe (Eucl.) spacetime
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