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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
May 2017
Astrid Eichhorn University of Heidelberg
A. Platania: Cosmic censorship in QEG
F. Saueressig: Cosmic perturbations from Asymptotic Safety
!
!
Starting point: Singularities• Incompleteness of General Relativity
• Incompleteness of the Standard Model of particle physics
k
e2HkL
Starting point: Singularities• Incompleteness of General Relativity
• Incompleteness of the Standard Model of particle physics
Fundamental description of spacetime needs QFT and QFTs of matter need gravity
!
k
e2HkL
Starting point: Singularities• Incompleteness of General Relativity
• Incompleteness of the Standard Model of particle physics
!Z
Dgµ⌫ D�StandardModeleiS[gµ⌫ ,�]goal:
Starting point: Singularities• Incompleteness of General Relativity
• Incompleteness of the Standard Model of particle physics
!Z
Dgµ⌫ D�StandardModeleiS[gµ⌫ ,�]goal:
quantum fluctuations) scale dependent (running) couplings
example: Quantum Electrodynamics quantum vacuum = screening medium
k
e2HkL
{ 1/ke+(k)
Starting point: Singularities• Incompleteness of General Relativity
• Incompleteness of the Standard Model of particle physics
!Z
Dgµ⌫ D�StandardModeleiS[gµ⌫ ,�]goal:
quantum fluctuations) scale dependent (running) couplings
{ 1/ke+(k)example: Quantum Electrodynamics quantum vacuum = screening medium
k
e2HkL
) qm fluc’s of metric: scale dependent grav. coupling
High-energy behavior in QFTs
CMS ‘14
running coupling in QCD: Asymptotic freedom
asymptotically: scale-invariance without interactions
[Gross, Wilczek; Politzer ’73]
High-energy behavior in QFTs
CMS ‘14
running coupling in QCD: Asymptotic freedom
asymptotically: scale-invariance without interactions
running coupling in QED: Landau pole/triviality
{ 1/ke+(k)[Gell-Mann, Low ’54; Gockeler et al. ’97;
Gies, Jaeckel ‘04]
[Gross, Wilczek; Politzer ’73]
new physics!k
e2HkL
⇤
High-energy behavior in QFTs
CMS ‘14
running coupling in QCD: Asymptotic freedom
asymptotically: scale-invariance without interactions
running coupling in QED: Landau pole/triviality
{ 1/ke+(k)[Gell-Mann, Low ’54; Gockeler et al. ’97;
Gies, Jaeckel ‘04]
[Gross, Wilczek; Politzer ’73]
new physics!k
e2HkL
⇤
& Higgs quartic coupling affected
U(1)hyperchargein Standard Model:
High-energy behavior in QFTs
CMS ‘14
running coupling in QCD: Asymptotic freedom
asymptotically: scale-invariance without interactions
running coupling in QED: Landau pole/triviality
{ 1/ke+(k)new physics!
k
e2HkL
⇤
[Gross, Wilczek; Politzer ’73]
Asymptotic safety
asymptotically: scale-invariance with interactions
[Weinberg ’76]
[Gell-Mann, Low ’54; Gockeler et al. ’97; Gies, Jaeckel ‘04]
Log[k]
G[k]
High-energy behavior in QFTs
CMS ‘14
running coupling in QCD: Asymptotic freedom
asymptotically: scale-invariance without interactions
running coupling in QED: Landau pole/triviality
{ 1/ke+(k)new physics!
k
e2HkL
⇤
Asymptotic safety
asymptotically: scale-invariance with interactions
[Gell-Mann, Low ’54; Gockeler et al. ’97; Gies, Jaeckel ‘04]
running coupling in gravity?
Log[k]
G[k]
[Gross, Wilczek; Politzer ’73]
[Weinberg ’76]
High-energy behavior in QFTs
CMS ‘14
running coupling in QCD: Asymptotic freedom
asymptotically: scale-invariance without interactions
running coupling in QED: Landau pole/triviality
{ 1/ke+(k)new physics!
k
e2HkL
⇤
Asymptotic safety
asymptotically: scale-invariance with interactions
[Gell-Mann, Low ’54; Gockeler et al. ’97; Gies, Jaeckel ‘04]
running coupling in gravity?
Log[k]
G[k]
[Gross, Wilczek; Politzer ’73]
[Weinberg ’76]
Quantum-field theoretic description of fundamental microscopic structure
of spacetime
)
High-energy behavior in QFTs
CMS ‘14
running coupling in QCD: Asymptotic freedom
asymptotically: scale-invariance without interactions
running coupling in QED: Landau pole/triviality
{ 1/ke+(k)new physics!
k
e2HkL
⇤
Asymptotic safety
asymptotically: scale-invariance with interactions
[Gell-Mann, Low ’54; Gockeler et al. ’97; Gies, Jaeckel ‘04]
running coupling in gravity?
Log[k]
G[k]
[Gross, Wilczek; Politzer ’73]
[Weinberg ’76]
qm fluc’s of gravity: sizeable for cannot probe running coupling directly (yet?)
E ⇡ MPlanck)
Functional Renormalization Group - zooming in on quantum spacetime
Functional Renormalization Group - zooming in on quantum spacetime
�k
S
contains effect of quantum fluctuations above k
�k!0
probe scale dependence of QFT
UV scale-invariant regime
classical regim
eLog[k]
G[k]
Functional Renormalization Group - zooming in on quantum spacetime
Wetterich ’93; Morris, ‘94
e��k[�] =
ZD' e�S[']� 12
R'(�p)Rk(p)'(p)
scale- and momentum- dependent ``mass”:
dials ``resolution scale”
probe scale dependence of QFT
�k
S
�k!0
contains effect of quantum fluctuations above k
Functional Renormalization Group - zooming in on quantum spacetime
Wetterich ’93; Morris, ‘94
e��k[�] =
ZD' e�S[']� 12
R'(�p)Rk(p)'(p)
scale- and momentum- dependent ``mass”:
dials ``resolution scale”
probe scale dependence of QFT
�k
S
�k!0
contains effect of quantum fluctuations above k @k�k =
1
2STr
⇣�(2)k +Rk
⌘�1@kRk
Wetterich equation:
=
Asymptotic safety for quantum gravity
-0.1 0.0 0.1 0.2 0.3 0.4 0.5-0.1
0.0
0.1
0.2
0.3
0.4
l
G
�k = �1
16⇡GN (k)
Zd
4x
pg (R� 2�̄(k)) G(k) = GN (k)k2, �(k) = �̄(k)/k2
Reuter, ’96; Reuter, Saueressig ‘01, Litim, ‘03
towards IR
Asymptotic safety for quantum gravity
-0.1 0.0 0.1 0.2 0.3 0.4 0.5-0.1
0.0
0.1
0.2
0.3
0.4
l
G
�k = �1
16⇡GN (k)
Zd
4x
pg (R� 2�̄(k)) G(k) = GN (k)k2, �(k) = �̄(k)/k2
Log[k]
G[k]
Reuter, ’96; Reuter, Saueressig ‘01, Litim, ‘03
towards IRUV scale-invariant regime
k @kG(k) = 0
Asymptotic safety for quantum gravity
-0.1 0.0 0.1 0.2 0.3 0.4 0.5-0.1
0.0
0.1
0.2
0.3
0.4
l
G
�k = �1
16⇡GN (k)
Zd
4x
pg (R� 2�̄(k)) G(k) = GN (k)k2, �(k) = �̄(k)/k2
classical regime
Log[k]
G[k]
GN (k) = constReuter, ’96; Reuter, Saueressig ‘01, Litim, ‘03
towards IRUV scale-invariant regime
k @kG(k) = 0
Asymptotic safety for quantum gravity
-0.1 0.0 0.1 0.2 0.3 0.4 0.5-0.1
0.0
0.1
0.2
0.3
0.4
l
G
�k = �1
16⇡GN (k)
Zd
4x
pg (R� 2�̄(k)) G(k) = GN (k)k2, �(k) = �̄(k)/k2
Reuter, ’96; Reuter, Saueressig ‘01, Litim, ‘03
quantum fluctuations of metric generate additional terms in the microscopic dynamics
�k = �EH
+a
Zd
4x
pgR
2 + b
Zd
4x
pgRµ⌫R
µ⌫ + c
Zd
4x
pgR⇤R+ ...
finite number of free parameters (= predictivity) finite number of UV attractive directions A.S. predicts values of all other couplings!)
Asymptotic safety for quantum gravity
-0.1 0.0 0.1 0.2 0.3 0.4 0.5-0.1
0.0
0.1
0.2
0.3
0.4
l
G
�k = �1
16⇡GN (k)
Zd
4x
pg (R� 2�̄(k))
Reuter, ’96; Reuter, Saueressig ‘01, Litim, ‘03
G(k) = GN (k)k2, �(k) = �̄(k)/k2
R2, Rµ⌫Rµ⌫ Benedetti, Machado, Saueressig, ‘09
C �µ⌫ C⇢�
� Cµ⌫
⇢� Gies, Knorr, Lippoldt, Saueressig ‘16
perturbative counterterms: asymptotic safety
Christiansen, ’16, Oda, Yamada ‘17
Reuter, Lauscher, ’02; Codello, Percacci, Rahmede, ’09; Benedetti, Caravelli, ’12; Dietz, Morris, ’12;
Falls, Litim, Nikolakopoulos, Rahmede, ’13, ‘14 Demmel, Saueressig, Zanusso, ’15; Eichhorn ‘15
f(R) =NX
n=0
anRn
extended tests:
’t Hooft, Veltman ’74; Deser, Niewenhuizen ’74; Christensen, Duff ’80;
Goroff, Sagnotti ’85, ’86; Van de Ven ‘92
Asymptotic safety for quantum gravity
-0.1 0.0 0.1 0.2 0.3 0.4 0.5-0.1
0.0
0.1
0.2
0.3
0.4
l
G
�k = �1
16⇡GN (k)
Zd
4x
pg (R� 2�̄(k))
Reuter, ’96; Reuter, Saueressig ‘01, Litim, ‘03
G(k) = GN (k)k2, �(k) = �̄(k)/k2
R2, Rµ⌫Rµ⌫ Benedetti, Machado, Saueressig, ‘09
C �µ⌫ C⇢�
� Cµ⌫
⇢� Gies, Knorr, Lippoldt, Saueressig ‘16
perturbative counterterms: asymptotic safety
Christiansen, ’16, Oda, Yamada ‘17
Reuter, Lauscher, ’02; Codello, Percacci, Rahmede, ’09; Benedetti, Caravelli, ’12; Dietz, Morris, ’12;
Falls, Litim, Nikolakopoulos, Rahmede, ’13, ‘14 Demmel, Saueressig, Zanusso, ’15; Eichhorn ‘15
f(R) =NX
n=0
anRn
extended tests:
’t Hooft, Veltman ’74; Deser, Niewenhuizen ’74; Christensen, Duff ’80;
Goroff, Sagnotti ’85, ’86; Van de Ven ‘92
compelling hints for existence of
UV scale invariance in quantum gravity
Asymptotic safety for quantum gravity
-0.1 0.0 0.1 0.2 0.3 0.4 0.5-0.1
0.0
0.1
0.2
0.3
0.4
l
G
�k = �1
16⇡GN (k)
Zd
4x
pg (R� 2�̄(k)) G(k) = GN (k)k2, �(k) = �̄(k)/k2
Reuter, ’96; Reuter, Saueressig ‘01, Litim, ‘03
quantum fluctuations of metric generate additional terms in the microscopic dynamics
�k = �EH
+a
Zd
4x
pgR
2 + b
Zd
4x
pgRµ⌫R
µ⌫ + c
Zd
4x
pgR⇤R+ ...
! observational constraints ? (e.g. grav. waveforms)
microscopic values = fixed-point values
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�@� �r2
�P (x, x0,�) = 0
Microscopic structure of spacetime: Hints for dimensional reduction to 2
Probe (Eucl.) spacetime by a fictitious diffusing particle:
classically: spectral dimension from return probability�@� �r2
�P (x, x0,�) = 0
ds = �2@lnP (x, x,�)
@ln�= 4
Microscopic structure of spacetime: Hints for dimensional reduction to 2
Probe (Eucl.) spacetime by a fictitious diffusing particle:
classically: spectral dimension from return probability
quantum-gravity regime: scale-invariance encoded in diffusion equation
�@� �r2
�P (x, x0,�) = 0
ds = �2@lnP (x, x,�)
@ln�= 4
Lauscher, Reuter ’05
Microscopic structure of spacetime: Hints for dimensional reduction to 2
Probe (Eucl.) spacetime by a fictitious diffusing particle:
classically: spectral dimension from return probability
quantum-gravity regime: scale-invariance encoded in diffusion equation
�@� �r2
�P (x, x0,�) = 0
ds = �2@lnP (x, x,�)
@ln�= 4
�@
p� �r2
�P (x, x0,�) = 0
Lauscher, Reuter ’05
Calcagni, A.E., Saueressig, ‘13ds = 2
Microscopic structure of spacetime: Hints for dimensional reduction to 2
Probe (Eucl.) spacetime by a fictitious diffusing particle:
classically: spectral dimension from return probability
quantum-gravity regime: scale-invariance encoded in diffusion equation
�@� �r2
�P (x, x0,�) = 0
ds = �2@lnP (x, x,�)
@ln�= 4
�@
p� �r2
�P (x, x0,�) = 0
Lauscher, Reuter ’05
Calcagni, A.E., Saueressig, ‘13ds = 2
dimensional reduction: common theme in quantum gravityAmbjorn, 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
-0.1 0.0 0.1 0.2 0.3 0.4 0.5-0.1
0.0
0.1
0.2
0.3
0.4
l
G
Asymptotic safety for quantum gravity and matter
quantum gravity dynamics matter dynamics
Can quantum fluctuations of matter destroy
consistent quantum gravity model?
Matter matters�G = 2G+
G2
6⇡(�46 +NS + 2ND � 4NV ) + ...k @kG(k) =
quantum fluctuationscanonical scaling [G]=-2
Matter matters�G = 2G+
G2
6⇡(�46 +NS + 2ND � 4NV ) + ...k @kG(k) =
UV#a%rac(ve+fixed+point+
UV#repulsive+fixed+point+
-0.4 0.4 G
-3
-2
-1
1
2
3bG
canonical scaling [G]=-2
quantum fluctuations
asymptotic safety
Matter matters
10 20 30 40 50 60 70NS
10
20
30
40
ND
approximation: Einstein-Hilbert & minimally coupled matter
[Dona, AE, Percacci ’13, ‘14]
(@ 12 NV)
�G = 2G+G2
6⇡(�46 +NS + 2ND � 4NV ) + ...k @kG(k) =
scalars (Higgs)
fermions (quarks & leptons)
vectors (gauge bosons)
Matter matters
10 20 30 40 50 60 70NS
10
20
30
40
ND
�G = 2G+G2
6⇡(�46 +NS + 2ND � 4NV ) + ...k @kG(k) =
scalars (Higgs)
fermions (quarks & leptons)
vectors (gauge bosons)
approximation: Einstein-Hilbert & minimally coupled matter
[Dona, AE, Percacci ’13, ‘14]
Standard Model matter content compatible with asymptotically safe quantum gravity
(@ 12 NV)
-0.1 0.0 0.1 0.2 0.3 0.4 0.5-0.1
0.0
0.1
0.2
0.3
0.4
l
G
Asymptotic safety for quantum gravity and matter
quantum gravity dynamics matter dynamics
Can quantum fluctuations of matter destroy
consistent quantum gravity model?
Can quantum fluctuations of gravity generate
a viable UV completion for matter?
-0.1 0.0 0.1 0.2 0.3 0.4 0.5-0.1
0.0
0.1
0.2
0.3
0.4
l
G
Asymptotic safety for quantum gravity and matter
quantum gravity dynamics matter dynamics
Can quantum fluctuations of matter destroy
consistent quantum gravity model?
Can quantum fluctuations of gravity generate
a viable UV completion for matter?
triviality in Higgs & U(1)
MPlanckk
g
-0.1 0.0 0.1 0.2 0.3 0.4 0.5-0.1
0.0
0.1
0.2
0.3
0.4
l
G
Asymptotic safety for quantum gravity and matter
quantum gravity dynamics matter dynamics
Can quantum fluctuations of matter destroy
consistent quantum gravity model?
Can quantum fluctuations of gravity generate
a viable UV completion for matter?
MPlanckk
g
QG-induced asymptotic safety
?QG generated fixed point
triviality in Higgs & U(1)
-0.1 0.0 0.1 0.2 0.3 0.4 0.5-0.1
0.0
0.1
0.2
0.3
0.4
l
G
Asymptotic safety for quantum gravity and matter
quantum gravity dynamics matter dynamics
Can quantum fluctuations of matter destroy
consistent quantum gravity model?
Can quantum fluctuations of gravity generate
a viable UV completion for matter?
MPlanckk
g
QG-induced asymptotic freedom
QG-induced asymptotic safety
QG generated fixed point
?
triviality in Higgs & U(1)
-0.1 0.0 0.1 0.2 0.3 0.4 0.5-0.1
0.0
0.1
0.2
0.3
0.4
l
G
Asymptotic safety for quantum gravity and matter
quantum gravity dynamics matter dynamics
Can quantum fluctuations of matter destroy
consistent quantum gravity model?
Can quantum fluctuations of gravity generate
a viable UV completion for matter?
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 massMH ' 126 GeV [1], which further study has shown to be compatible with the properties expectedfor 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 thistypically translates into bounds on the mass scale of different BSM scenarios, supersymmetric orotherwise, of order the TeV [3]. If one is willing to hold on to the paradigm of naturalness, thehierarchy problem that afflicts the breaking of the electroweak (EW) symmetry would imply thatBSM physics should be around the corner, probably on the reach of the LHC. In this talk I take adifferent attitude: I disregard naturalness as a requisite for the physics associated to the breaking ofthe EW symmetry and I explore the possibility that the scale of new physics, L, could be as largeas the Planck scale, MPl .
From that perspective, we have now in our hands a quantum field theory, the SM, that shouldthen describe physics in the huge range from MW to MPl . All the model parameters have beendetermined experimentally, the last of them being the Higgs quartic coupling, fixed in this modelby our knowledge of the Higgs mass. Fig. 1, left plot, shows the running of the most important SMcouplings extrapolated to very high energy scales using renormalization group (RG) techniques. Itshows the three SU(3)C ⇥ SU(2)L ⇥U(1)Y gauge couplings getting closer in the ultraviolet (UV)but failing to unify precisely. It also shows how the top Yukawa coupling gets weaker in the UV(due to as effects, see below). The Higgs quartic coupling is also shown: it starts small at the EW
102 104 106 108 1010 1012 1014 1016 1018 1020
0.0
0.2
0.4
0.6
0.8
1.0
RGE scale m in GeV
SMcouplings
g1
g2
g3yt
lyb
102 104 106 108 1010 1012 1014 1016 1018 1020-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
RGE scale m in GeV
Hig
gsqu
artic
coup
lingl
3s bands inMt = 173.1 ± 0.6 GeV HgrayLa3HMZL = 0.1184 ± 0.0007HredLMh = 125.7 ± 0.3 GeV HblueL
Mt = 171.3 GeV
asHMZL = 0.1163asHMZL = 0.1205
Mt = 174.9 GeV
Figure 1: Left: Evolution of SM couplings from the EW scale to MPl. Right: Zoom on the evolution of theHiggs quartic, l (µ), for Mh = 125.7 GeV, with uncertainties in the top mass, as and Mh as indicated. (Plotstaken from [9]).
2
MPlanckk
g
Buttazzo et al. ‘13
QG-induced asymptotic freedom
QG-induced asymptotic safety
match onto SM at Planck scale
QG generated fixed point
?
triviality in Higgs & U(1)
Asymptotically safe gravity & the Standard Model *
* (truncated RG flow)
fixed point at vanishing potential[Narain, Percacci ’09; A.E. ’13; Percacci, Vacca ‘15]
! Higgs mass [Shaposhnikov, Wetterich ‘09 ]
& 126GeV
Asymptotically safe gravity & the Standard Model *
* (truncated RG flow)
fixed point at vanishing potential[Narain, Percacci ’09; A.E. ’13; Percacci, Vacca ‘15]
! Higgs mass [Shaposhnikov, Wetterich ‘09 ]
& 126GeV
y⇤ = 0 only admits for restricted UV-values of grav. couplings
!``pheno” constraint on QG[A.E., Held, Pawlowski ’16; A.E., Held ‘17]
mtop
= 176GeV
Asymptotically safe gravity & the Standard Model *
* (truncated RG flow)
fixed point at vanishing potential[Narain, Percacci ’09; A.E. ’13; Percacci, Vacca ‘15]
! Higgs mass [Shaposhnikov, Wetterich ‘09 ]
& 126GeV
chiral structure (light fermions) preserved[A.E., Gies ’11; Meibohm, Pawlowski ’16; A.E., Lippoldt ‘16]
y⇤ = 0 only admits for restricted UV-values of grav. couplings
!``pheno” constraint on QG[A.E., Held, Pawlowski ’16; A.E., Held ‘17]
mtop
= 176GeV
Asymptotically safe gravity & the Standard Model *
* (truncated RG flow)
fixed point at vanishing potential[Narain, Percacci ’09; A.E. ’13; Percacci, Vacca ‘15]
! Higgs mass [Shaposhnikov, Wetterich ‘09 ]
& 126GeV
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
y⇤ = 0 only admits for restricted UV-values of grav. couplings
``pheno” constraint on QG[A.E., Held, Pawlowski ’16; A.E., Held ‘17]
mtop
= 176GeV
Asymptotically safe gravity & the Standard Model *
[A.E., Gies ’11; Meibohm, Pawlowski ’16; A.E., Lippoldt ‘16]
* (truncated RG flow)
Asymptotically safe solution to the U(1) triviality problemQuantum- Gravity effects on U(1) gauge theory *:
* (truncated RG flow)
Asymptotically safe solution to the U(1) triviality problemQuantum- Gravity effects on U(1) gauge theory *:
• 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 = �e
4⇡G+
e3
12⇡2+ ...
-40 -20 0 20 40 60 80 1000.000
0.002
0.004
0.006
0.008
ln[k/MPlanck]
e[k]
-40 -20 0 20 40 60 80 1000.0
0.2
0.4
0.6
ln[k/MPlanck]
G[k]
* (truncated RG flow)
Asymptotically safe solution to the U(1) triviality problemQuantum- Gravity effects on U(1) gauge theory *:
• asymptotic freedom for the running charge
• asymptotic safety for induced photon-photon interactions
[Harst, Reuter ’11; Christiansen, A.E. ‘17]
[Christiansen, A.E. ‘17]
[Robinson, Wilczek 06; Pietrykowski ’07; Toms ’07, ’08, ’09, ’10,’11]
�e = �e
4⇡G+
e3
12⇡2+ ...
-40 -20 0 20 40 60 80 1000.000
0.002
0.004
0.006
0.008
ln[k/MPlanck]
e[k]
-40 -20 0 20 40 60 80 1000.0
0.2
0.4
0.6
ln[k/MPlanck]
G[k]
! w2 (F 2)2
* (truncated RG flow)
Quantum gravity fluctuations induce
new interactions beyond MPlanck
-80 -60 -40 -20 20w2
-50
50
100βw2
Asymptotically safe solution to the U(1) triviality problemQuantum- Gravity effects on U(1) gauge theory *:
• asymptotic freedom for the running charge
• asymptotic safety for induced photon-photon interactions
[Harst, Reuter ’11; Christiansen, A.E. ‘17]
[Christiansen, A.E. ‘17]
[Robinson, Wilczek 06; Pietrykowski ’07; Toms ’07, ’08, ’09, ’10,’11]
�e = �e
4⇡G+
e3
12⇡2+ ...
-40 -20 0 20 40 60 80 1000.000
0.002
0.004
0.006
0.008
ln[k/MPlanck]
e[k]
-40 -20 0 20 40 60 80 1000.0
0.2
0.4
0.6
ln[k/MPlanck]
G[k]
! w2 (F 2)2 G=0
* (truncated RG flow)
no photon self- interactions in the UV w/o qm gravity
-80 -60 -40 -20 20w2
-50
50
100βw2
Asymptotically safe solution to the U(1) triviality problemQuantum- Gravity effects on U(1) gauge theory *:
• asymptotic freedom for the running charge
• asymptotic safety for induced photon-photon interactions
[Harst, Reuter ’11; Christiansen, A.E. ‘17]
[Christiansen, A.E. ‘17]
[Robinson, Wilczek 06; Pietrykowski ’07; Toms ’07, ’08, ’09, ’10,’11]
�e = �e
4⇡G+
e3
12⇡2+ ...
-40 -20 0 20 40 60 80 1000.000
0.002
0.004
0.006
0.008
ln[k/MPlanck]
e[k]
-40 -20 0 20 40 60 80 1000.0
0.2
0.4
0.6
ln[k/MPlanck]
G[k]
! w2 (F 2)2 G=0G=1.6
QG generates finite photon
self-interactions (beyond MPlanck)
* (truncated RG flow)
Asymptotically safe solution to the U(1) triviality problem
• asymptotic freedom for the running charge
• asymptotic safety for induced photon-photon interactions
[Harst, Reuter ’11; Christiansen, A.E. ‘17]
[Christiansen, A.E. ‘17]
[Robinson, Wilczek 06; Pietrykowski ’07; Toms ’07, ’08, ’09, ’10,’11]
�e = �e
4⇡G+
e3
12⇡2+ ...
-40 -20 0 20 40 60 80 1000.000
0.002
0.004
0.006
0.008
ln[k/MPlanck]
e[k]
-40 -20 0 20 40 60 80 1000.0
0.2
0.4
0.6
ln[k/MPlanck]
G[k]
! w2 (F 2)2-80 -60 -40 -20 20
w2
-50
50
100βw2
G=0G=1.6
G=2.4
Quantum- Gravity effects on U(1) gauge theory *:* (truncated RG flow)
QG too strong: destruction of UV completion
for matter: divergence in
photon interactions
Asymptotically safe solution to the U(1) triviality problem
• asymptotic freedom for the running charge
• asymptotic safety for induced photon-photon interactions
[Harst, Reuter ’11; Christiansen, A.E. ‘17]
[Christiansen, A.E. ‘17]
[Robinson, Wilczek 06; Pietrykowski ’07; Toms ’07, ’08, ’09, ’10,’11]
�e = �e
4⇡G+
e3
12⇡2+ ...
-40 -20 0 20 40 60 80 1000.000
0.002
0.004
0.006
0.008
ln[k/MPlanck]
e[k]
-40 -20 0 20 40 60 80 1000.0
0.2
0.4
0.6
ln[k/MPlanck]
G[k]
! w2 (F 2)2-80 -60 -40 -20 20
w2
-50
50
100βw2
G=0G=1.6
G=2.4
weak-gravity bound: viable UV completion for matter only for weak QG
[A.E. ’13; A.E., Held, Pawlowski ’16; A.E., Held ‘17]
Quantum- Gravity effects on U(1) gauge theory *:* (truncated RG flow)
bound satisfied in all approximations
tested so far
SummaryAsymptotic safety paradigm: UV complete Quantum Field Theory of gravity and matter
-0.1 0.0 0.1 0.2 0.3 0.4 0.5-0.1
0.0
0.1
0.2
0.3
0.4
l
G
UV scale-invariant regime
classical regime
Log[k]
G[k]
GN (k) = constReuter, ’96; Reuter, Saueressig ‘01, Litim, ‘03
SummaryAsymptotic safety paradigm: UV complete Quantum Field Theory of gravity and matter
Hints for dynamical dimensional reduction in the UV ( scale invariance)$
SummaryAsymptotic safety paradigm: UV complete Quantum Field Theory of gravity and matter
Matter matters for the microscopic dynamics of spacetime
Hints for dynamical dimensional reduction in the UV ( scale invariance)$
10 20 30 40 50 60 70NS
10
20
30
40
ND
[Dona, AE, Percacci ’13, ‘14]
Standard Model matter content compatible with asymptotically safe quantum gravity
SummaryAsymptotic safety paradigm: UV complete Quantum Field Theory of gravity and matter
Matter matters for the microscopic dynamics of spacetime
Hints for dynamical dimensional reduction in the UV ( scale invariance)$
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
[ATLAS, CMS]
mh ⇡ 126GeV
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
[ATLAS, CMS]
mh ⇡ 126GeV
How does the Higgs mass tell us about
the scale of new physics?
mh
kRG scale 1019 GeV
strong coupling/triviality bound175GeV
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
[ATLAS, CMS]
mh ⇡ 126GeV
How does the Higgs mass tell us about
the scale of new physics?
[Maiani, Parisi, Petronzio ’78; Cabibo, Maiani, Parisi, Petronzio ’79;
Dashed, Neuberger ’83; Callaway ’84, Lindner ’86…]
mh
kRG scale
vacuum stability bound
1019 GeV
strong coupling/triviality bound175GeV⇡ 125GeV
measured Higgs mass
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
[ATLAS, CMS]
mh ⇡ 126GeV
How does the Higgs mass tell us about
the scale of new physics?
[Maiani, Parisi, Petronzio ’78; Cabibo, Maiani, Parisi, Petronzio ’79;
Dashed, Neuberger ’83; Callaway ’84, Lindner ’86…]
[Krive, Linde ’76; Krasnikov ’78; Hung ’79; Politzer, Wolfram ’79;
Linde ’80; Lindner, Sher, Zaglauer ’89;
Ford, Jones, Stephenson, Einhorn ’93…]
[Espinosa, Quiros ’95; Ellis, Espinosa, Giudice, Hoecker, Riotto ’09; Elias-Miro, Espinosa, Giudice, Isidori, Riotto, Strumia ’12;
Bezrukov, Kalmykov, Kniehl, Shaposhnikov ’12…]
Matter matters
�↵s = �✓11� 2
3Nf
◆↵2s2⇡
+ ...
analogy: destruction of asymptotic freedom by matter
gluons anti-screen
fermions screen
) antiscreening vacuum (asymptotic freedom) only for Nf . 16.5