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

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⌫ ,] goal: gµ⌫ Standard Modele ! D D Z Starting point: Singularities • Incompleteness of General Relativity

• Incompleteness of the Standard Model of particle physics e2 k

iS[gµ⌫ ,] goal: gµ⌫ Standard 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⌫ ,] goal: gµ⌫ Standard 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]

k contains effect of quantum ﬂuctuations above k

Log[k] k 0 ! classical regime Functional Renormalization Group - zooming in on quantum spacetime probe scale dependence of QFT

[] 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”

k contains effect of quantum ﬂuctuations above k

k 0 ! Functional Renormalization Group - zooming in on quantum spacetime probe scale dependence of QFT

[] 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 k 1 (2) ﬂuctuations above k @kk = STr + Rk @kRk 2 k ⇣ ⌘

= k 0 ! Asymptotic safety for quantum gravity 1 4 ¯ 2 ¯ 2 = d xpg (R 2(k)) G(k)=GN (k)k ,(k)=(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 = d xpg (R 2(k)) G(k)=GN (k)k ,(k)=(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]

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 = d xpg (R 2(k)) G(k)=GN (k)k ,(k)=(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

k =EH

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 = d xpg (R 2(k)) G(k)=GN (k)k ,(k)=(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 = d xpg (R 2(k)) G(k)=GN (k)k ,(k)=(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

0.3 quantum ﬂuctuations of metric 0.2 generate additional terms G in the microscopic dynamics 0.1

k =EH

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,)=0 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,)=0 r @lnP (x, x, ) d = 2 =4 s @ln Microscopic structure of spacetime: Hints for dimensional reduction to 2

Probe (Eucl.) spacetime by a ﬁctitious diffusing particle:

classically: quantum-gravity regime: spectral dimension scale-invariance encoded in from return probability diffusion equation Lauscher, Reuter ’05

2 @ P (x, x0,)=0 r @lnP (x, x, ) d = 2 =4 s @ln Microscopic structure of spacetime: Hints for dimensional reduction to 2

Probe (Eucl.) spacetime by a ﬁctitious diffusing particle:

classically: quantum-gravity regime: spectral dimension scale-invariance encoded in from return probability diffusion equation Lauscher, Reuter ’05 2 @ P (x, x0,)=0 2 p @ P (x, x0,)=0 r d =2 Calcagni, A.E., Saueressig, ‘13 r s @lnP (x, x, ) d = 2 =4 s @ln Microscopic structure of spacetime: Hints for dimensional reduction to 2

Probe (Eucl.) spacetime by a ﬁctitious diffusing particle:

classically: quantum-gravity regime: spectral dimension scale-invariance encoded in from return probability diffusion equation Lauscher, Reuter ’05 2 @ P (x, x0,)=0 2 p @ P (x, x0,)=0 r d =2 Calcagni, A.E., Saueressig, ‘13 r s @lnP (x, x, ) dimensional reduction: d = 2 =4 s @ln common theme in quantum gravity Ambjorn, Jurkiewicz, Loll ’05; Carlip ’09; Horava ’09…. Microscopic structure of spacetime: Hints for dimensional reduction to 2

Cosmic censorship in QEG

talk by A. Platania !

Cosmic perturbations from Asymptotic Safety

talk by F. Saueressig ! Asymptotic safety for quantum gravity and matter

quantum gravity dynamics matter dynamics Asymptotic safety for quantum gravity and matter

0.4

Can quantum ﬂuctuations 0.3

of matter destroy 0.2 G consistent quantum gravity model? 0.1

0.0

-0.1 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 l

quantum gravity dynamics matter dynamics Matter matters G2 k@kG(k)= =2G + ( 46 + N +2N 4N )+... G 6⇡ S D V canonical scaling quantum ﬂuctuations [G]=-2 Matter matters G2 k@kG(k)= =2G + ( 46 + N +2N 4N )+... G 6⇡ S D V bG 3 canonical scaling quantum ﬂuctuations 2

[G]=-2 1

G -0.4 0.4 -1 UV#repulsive+asymptotic ﬁxed+point+ -2 safetyUV#a%rac(ve+ -3 ﬁxed+point+ Matter matters G2 k@kG(k)= =2G + ( 46 + N +2N 4N )+... G 6⇡ S D V N D 40 vectors scalars fermions (gauge bosons) (Higgs) (quarks & leptons) 30

(@ 12 NV) 10

N 10 20 30 40 50 60 70 S [Dona, AE, Percacci ’13, ‘14]

approximation: Einstein-Hilbert & minimally coupled matter Matter matters G2 k@kG(k)= =2G + ( 46 + N +2N 4N )+... G 6⇡ S D V N D 40 vectors scalars fermions (gauge bosons) (Higgs) (quarks & leptons) 30 Standard Model matter content compatible with asymptotically safe quantum gravity 20

(@ 12 NV) 10

N 10 20 30 40 50 60 70 S [Dona, AE, Percacci ’13, ‘14]

approximation: Einstein-Hilbert & minimally coupled matter Asymptotic safety for quantum gravity and matter

0.4

Can quantum ﬂuctuations 0.3

of matter destroy 0.2 G consistent quantum gravity model? 0.1

0.0

-0.1 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 l

quantum gravity dynamics matter dynamics

Can quantum ﬂuctuations of gravity generate a viable UV completion for matter? Asymptotic safety for quantum gravity and matter

0.4

Can quantum ﬂuctuations 0.3

of matter destroy 0.2 G consistent quantum gravity model? 0.1

0.0

-0.1 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 l

quantum gravity dynamics matter dynamics

triviality in Higgs & U(1)

Can quantum ﬂuctuations of gravity generate g a viable UV completion for matter?

k MPlanck Asymptotic safety for quantum gravity and matter

0.4

Can quantum ﬂuctuations 0.3

of matter destroy 0.2 G consistent quantum gravity model? 0.1

0.0

-0.1 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 l

quantum gravity dynamics matter dynamics

triviality in Higgs & U(1)

QG-induced Can quantum ﬂuctuations asymptotic safety of gravity generate g a viable UV completion for matter?

QG generated ? ﬁxed point k MPlanck Asymptotic safety for quantum gravity and matter

0.4

Can quantum ﬂuctuations 0.3

of matter destroy 0.2 G consistent quantum gravity model? 0.1

0.0

-0.1 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 l

quantum gravity dynamics matter dynamics

triviality in Higgs & U(1)

QG-induced Can quantum ﬂuctuations asymptotic safety of gravity generate g QG-induced a viable UV completion for matter? asymptotic freedom

QG generated ? ﬁxed point k MPlanck Vacuum stability and the Higgs Boson

1. Extrapolating the SM to Very High Scales and the Higgs Potential Instability

The main result of the first run of the LHC was the discovery of the Higgs boson, with mass M 126 GeV [1], which further study has shown to be compatible with the properties expected H ' for a Standard Model (SM) Higgs, although there is still room for some deviation in its properties [2]. Besides this great success, no trace of physics beyond the SM (BSM) has been found, and this typically translates into bounds on the mass scale of different BSM scenarios, supersymmetric or otherwise, of order the TeV [3]. If one is willing to hold on to the paradigm of naturalness, the hierarchyAsymptotic problem that afflicts the breaking safety of the electroweak for (EW) quantum symmetry would imply that gravity and matter BSM physics should be around the corner, probably on the reach of the LHC. In this talk I take a different attitude: I disregard naturalness as a requisite for the physics associated to the breaking of 0.4 the EW symmetry and I explore the possibility that the scale of new physics, L, could be as large Can quantum fluctuations 0.3 as the Planck scale, MPl. From that perspective, we have now in our hands a quantumof matter field theory, destroy the SM, that should 0.2 G then describe physics in the huge range fromconsistentMW to MPl. All quantum the model parameters gravity have model? been 0.1 determined experimentally, the last of them being the Higgs quartic coupling, fixed in this model 0.0 by our knowledge of the Higgs mass. Fig. 1, left plot, shows the running of the most important SM -0.1 couplings extrapolated to very high energy scales using renormalization group (RG) techniques. It -0.1 0.0 0.1 0.2 0.3 0.4 0.5 shows the three SU (3) SU (2) U(1) gauge couplings getting closer in the ultraviolet (UV) l C ⇥ L ⇥ Y but failing to unify precisely. It also shows how the top Yukawa coupling gets weaker in the UV (due toquantumas effects, see below). gravity The Higgs quarticdynamics coupling is also shown: it starts small at the EW matter dynamics

triviality in Higgs & U(1) 1.0 0.10

g3 3s bands in yt 0.08 0.8 Mt = 173.1 ± 0.6 GeV gray QG-induced a3 MZ = 0.1184 ± 0.0007 red 0.06 l Can quantumMh = 125.7 ±ﬂuctuations 0.3 GeV blue asymptotic safety H L 0.6 g2 g 0.04 of gravityH L generateH L coupling H L g1 QG-induced couplings 0.4 a viable0.02 UV completion for matter? quartic asymptotic freedom SM Mt = 171.3 GeV

Higgs 0.00 0.2 as MZ = 0.1205

-0.02 as MZ = 0.1163 l MtH = 174.9L GeV 0.0 yb match onto SM QG generated -0.04 ? H L 102 104 106 108 1010 1012 1014 1016 1018 1020 at Planck102 10scale4 106 108 1010 1012 1014ﬁxed1016 10 point18 1020 RGE scale m in GeV RGE scale m in GeV k MPlanck Buttazzo et al. ‘13 Figure 1: Left: Evolution of SM couplings from the EW scale to MPl. Right: Zoom on the evolution of the Higgs quartic, l(µ), for Mh = 125.7 GeV, with uncertainties in the top mass, as and Mh as indicated. (Plots taken from [9]).

2 Asymptotically safe gravity & the Standard Model *

* (truncated RG ﬂow) Asymptotically safe gravity & the Standard Model *

ﬁxed point at vanishing potential [Narain, Percacci ’09; A.E. ’13; Percacci, Vacca ‘15]

Higgs mass & 126 GeV ! [Shaposhnikov, Wetterich ‘09 ] * (truncated RG ﬂow) Asymptotically safe gravity & the Standard Model *

y =0 only admits m top = 176 GeV ⇤ for restricted UV-values of grav. couplings ``pheno” constraint on QG ! [A.E., Held, Pawlowski ’16; A.E., Held ‘17]

ﬁxed point at vanishing potential [Narain, Percacci ’09; A.E. ’13; Percacci, Vacca ‘15]

Higgs mass & 126 GeV ! [Shaposhnikov, Wetterich ‘09 ] * (truncated RG ﬂow) Asymptotically safe gravity & the Standard Model *

chiral structure (light fermions) preserved

[A.E., Gies ’11; Meibohm, Pawlowski ’16; A.E., Lippoldt ‘16]

y =0 only admits m top = 176 GeV ⇤ for restricted UV-values of grav. couplings ``pheno” constraint on QG ! [A.E., Held, Pawlowski ’16; A.E., Held ‘17]

ﬁxed point at vanishing potential [Narain, Percacci ’09; A.E. ’13; Percacci, Vacca ‘15]

Higgs mass & 126 GeV ! [Shaposhnikov, Wetterich ‘09 ] * (truncated RG ﬂow) Asymptotically safe gravity & the Standard Model *

asymptotically safe solution to the Landau pole/ triviality problem in U(1)? [Daum, Harst, Reuter ’09; Harst, Reuter ’11; Folkerts, Litim, Pawlowski ’11; Christiansen, A.E. ‘17] chiral structure (light fermions) preserved

[A.E., Gies ’11; Meibohm, Pawlowski ’16; A.E., Lippoldt ‘16]

y =0 only admits m top = 176 GeV ⇤ for restricted UV-values of grav. couplings ``pheno” constraint on QG [A.E., Held, Pawlowski ’16; A.E., Held ‘17]

ﬁxed point at vanishing potential [Narain, Percacci ’09; A.E. ’13; Percacci, Vacca ‘15]

Higgs mass & 126 GeV ! [Shaposhnikov, Wetterich ‘09 ] * (truncated RG flow) Asymptotically safe solution to the U(1) triviality problem Quantum- Gravity effects on U(1) gauge theory *: * (truncated RG flow) Asymptotically safe solution to the U(1) triviality problem Quantum- Gravity effects on U(1) gauge theory *: * (truncated RG flow) • asymptotic freedom for the running charge [Harst, Reuter ’11; Christiansen, A.E. ‘17] [Robinson, Wilczek 06; Pietrykowski ’07; Toms ’07, ’08, ’09, ’10,’11] e e3 e = G + 2 + ... 0.6 0.008 4⇡ 12⇡ 0.006 k ] [ 0.4 k ] [ G e 0.004 0.2 0.002

0.0 0.000 -40 -20 0 20 40 60 80 100 -40 -20 0 20 40 60 80 100 ln[k/MPlanck] ln[k/MPlanck] Asymptotically safe solution to the U(1) triviality problem Quantum- Gravity effects on U(1) gauge theory *: * (truncated RG ﬂow) • asymptotic freedom for the running charge [Harst, Reuter ’11; Christiansen, A.E. ‘17] [Robinson, Wilczek 06; Pietrykowski ’07; Toms ’07, ’08, ’09, ’10,’11] e e3 e = G + 2 + ... 0.6 0.008 4⇡ 12⇡ 0.006 k ] [ 0.4 k ] [ G e 0.004 0.2 0.002

0.0 0.000 -40 -20 0 20 40 60 80 100 -40 -20 0 20 40 60 80 100 ln[k/MPlanck] ln[k/MPlanck] • asymptotic safety for induced photon-photon interactions [Christiansen, A.E. ‘17]

Quantum gravity ﬂuctuations induce new interactions 2 2 w (F ) beyond MPlanck ! 2 Asymptotically safe solution to the U(1) triviality problem Quantum- Gravity effects on U(1) gauge theory *: * (truncated RG ﬂow) • asymptotic freedom for the running charge [Harst, Reuter ’11; Christiansen, A.E. ‘17] [Robinson, Wilczek 06; Pietrykowski ’07; Toms ’07, ’08, ’09, ’10,’11] e e3 e = G + 2 + ... 0.6 0.008 4⇡ 12⇡ 0.006 k ] [ 0.4 k ] [ G e 0.004 0.2 0.002

0.0 0.000 -40 -20 0 20 40 60 80 100 -40 -20 0 20 40 60 80 100 ln[k/MPlanck] ln[k/MPlanck] • asymptotic safety for induced photon-photon interactions [Christiansen, A.E. ‘17] βw2 100 no photon self- 50 interactions in the UV w/o qm gravity w2 -80 -60 -40 -20 20 2 2 w (F ) G=0-50 ! 2 Asymptotically safe solution to the U(1) triviality problem Quantum- Gravity effects on U(1) gauge theory *: * (truncated RG ﬂow) • asymptotic freedom for the running charge [Harst, Reuter ’11; Christiansen, A.E. ‘17] [Robinson, Wilczek 06; Pietrykowski ’07; Toms ’07, ’08, ’09, ’10,’11] e e3 e = G + 2 + ... 0.6 0.008 4⇡ 12⇡ 0.006 k ] [ 0.4 k ] [ G e 0.004 0.2 0.002

0.0 0.000 -40 -20 0 20 40 60 80 100 -40 -20 0 20 40 60 80 100 ln[k/MPlanck] ln[k/MPlanck] • asymptotic safety for induced photon-photon interactions [Christiansen, A.E. ‘17] βw2 100 QG generates 50 ﬁnite photon self-interactions w2 -80 -60 -40 -20 20 (beyond MPlanck) 2 2 w (F ) G=0 -50 ! 2 G=1.6 Asymptotically safe solution to the U(1) triviality problem Quantum- Gravity effects on U(1) gauge theory *: * (truncated RG ﬂow) • asymptotic freedom for the running charge [Harst, Reuter ’11; Christiansen, A.E. ‘17] [Robinson, Wilczek 06; Pietrykowski ’07; Toms ’07, ’08, ’09, ’10,’11] e e3 e = G + 2 + ... 0.6 0.008 4⇡ 12⇡ 0.006 k ] [ 0.4 k ] [ G e 0.004 0.2 0.002

w2 -80 -60 -40 -20 20 for matter: 2 2 divergence in w2 (F ) G=1.6 G=0 -50 ! photon interactions Asymptotically safe solution to the U(1) triviality problem Quantum- Gravity effects on U(1) gauge theory *: * (truncated RG ﬂow) • asymptotic freedom for the running charge [Harst, Reuter ’11; Christiansen, A.E. ‘17] [Robinson, Wilczek 06; Pietrykowski ’07; Toms ’07, ’08, ’09, ’10,’11] e e3 e = G + 2 + ... 0.6 0.008 4⇡ 12⇡ 0.006 k ] [ 0.4 k ] [ G e 0.004 0.2 0.002

w2 A.E., Held ‘17] -80 -60 -40 -20 20 2 2 bound satisﬁed in w (F ) G=0 -50 ! 2 G=1.6 all approximations tested so far Summary Asymptotic safety paradigm: UV complete Quantum Field Theory of gravity and matter

0.4

UV scale-invariant regime 0.3

0.2 G 0.1 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 Summary Asymptotic safety paradigm: UV complete Quantum Field Theory of gravity and matter

Hints for dynamical dimensional reduction in the UV ( scale invariance) $ Summary Asymptotic safety paradigm: UV complete Quantum Field Theory of gravity and matter

Hints for dynamical dimensional reduction in the UV ( scale invariance) $ Matter matters for the microscopic dynamics of spacetime N D 40

30 Standard Model matter content compatible with asymptotically safe quantum gravity 20

N 10 20 30 40 50 60 70 S [Dona, AE, Percacci ’13, ‘14] Summary Asymptotic safety paradigm: UV complete Quantum Field Theory of gravity and matter

Hints for dynamical dimensional reduction in the UV ( scale invariance) $ Matter matters for the microscopic dynamics of spacetime

Hints for quantum-gravity induced UV completion for the Standard Model of particle physics Starting point: Singularities • Incompleteness of General Relativity

• Incompleteness of the Standard Model of particle physics Where should we expect new physics? ! Possible interpretation of LHC data: New physics at the Planck scale Starting point: Singularities • Incompleteness of General Relativity

• Incompleteness of the Standard Model of particle physics Where should we expect new physics? ! Possible interpretation of LHC data: New physics at the Planck scale m 126 GeV h ⇡ [ATLAS, CMS] Starting point: Singularities • Incompleteness of General Relativity

• Incompleteness of the Standard Model of particle physics Where should we expect new physics? ! Possible interpretation of LHC data: New physics at the Planck scale m 126 GeV h ⇡ [ATLAS, CMS]

How does the Higgs mass tell us about the scale of new physics? Starting point: Singularities • Incompleteness of General Relativity

RG scale k 1019 GeV Starting point: Singularities • Incompleteness of General Relativity

• Incompleteness of the Standard Model of particle physics Where should we expect new physics? ! Possible interpretation of LHC data: New physics at the Planck scale m 126 GeV mh h ⇡ [ATLAS, CMS] measured Higgs mass [Maiani, Parisi, Petronzio ’78; Cabibo, Maiani, Parisi, Petronzio ’79; Dashed, Neuberger ’83; How does the Higgs Callaway ’84, Lindner ’86…] mass tell us about strong coupling/triviality bound 175 GeV 125 GeV [Krive, Linde ’76; Krasnikov ’78; the scale of new physics? ⇡ Hung ’79; Politzer, Wolfram ’79; vacuum stability bound Linde ’80; Lindner, Sher, Zaglauer ’89; [Espinosa, Quiros ’95; Ellis, Espinosa, Giudice, Hoecker, Riotto ’09; 19 Ford, Jones, Elias-Miro, Espinosa, Giudice, Isidori, Riotto, Strumia ’12; RG scale k 10 GeV Stephenson, Einhorn ’93…] Bezrukov, Kalmykov, Kniehl, Shaposhnikov ’12…] Matter matters analogy: destruction of asymptotic freedom by matter

2 ↵2 = 11 N s + ... ↵s 3 f 2⇡ ✓ ◆ gluons fermions anti-screen screen

antiscreening vacuum (asymptotic freedom) ) only for Nf . 16.5