The asymptotic safety paradigm for quantum spacetime and ......The asymptotic safety paradigm for...

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



Fundamental description of spacetime needs QFT and QFTs of matter need gravity

!

k

e2HkL



!Z

Dgµ⌫ D�StandardModeleiS[gµ⌫ ,�]goal:



!Z


quantum fluctuations) scale dependent (running) couplings

example: Quantum Electrodynamics quantum vacuum = screening medium

k

e2HkL

{ 1/ke+(k)



!Z


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]


CMS ‘14



running coupling in QED: Landau pole/triviality

{ 1/ke+(k)[Gell-Mann, Low ’54; Gockeler et al. ’97;

Gies, Jaeckel ‘04]


new physics!k

e2HkL

⇤


CMS ‘14




{ 1/ke+(k)[Gell-Mann, Low ’54; Gockeler et al. ’97;

Gies, Jaeckel ‘04]


new physics!k

e2HkL

⇤

& Higgs quartic coupling affected

U(1)hyperchargein Standard Model:


CMS ‘14




{ 1/ke+(k)new physics!

k

e2HkL

⇤


Asymptotic safety

asymptotically: scale-invariance with interactions

[Weinberg ’76]

[Gell-Mann, Low ’54; Gockeler et al. ’97; Gies, Jaeckel ‘04]

Log[k]

G[k]


CMS ‘14





k

e2HkL

⇤

Asymptotic safety



running coupling in gravity?

Log[k]

G[k]


[Weinberg ’76]


CMS ‘14





k

e2HkL

⇤

Asymptotic safety




Log[k]

G[k]


[Weinberg ’76]

Quantum-field theoretic description of fundamental microscopic structure

of spacetime

)


CMS ‘14





k

e2HkL

⇤

Asymptotic safety




Log[k]

G[k]


[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


�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]


Wetterich ’93; Morris, ‘94

e��k[�] =

ZD' e�S[']� 12

R'(�p)Rk(p)'(p)

scale- and momentum- dependent ``mass”:

dials ``resolution scale”


�k

S

�k!0

contains effect of quantum fluctuations above k


Wetterich ’93; Morris, ‘94

e��k[�] =

ZD' e�S[']� 12

R'(�p)Rk(p)'(p)

scale- and momentum- dependent ``mass”:

dials ``resolution scale”


�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


-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]


towards IRUV scale-invariant regime

k @kG(k) = 0


-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


-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


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!)


-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

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


-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

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


-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


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


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



classically: spectral dimension from return probability�@� �r2

�P (x, x0,�) = 0



classically: spectral dimension from return probability�@� �r2

�P (x, x0,�) = 0

ds = �2@lnP (x, x,�)

@ln�= 4



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





�@� �r2

�P (x, x0,�) = 0

ds = �2@lnP (x, x,�)

@ln�= 4

�@

p� �r2

�P (x, x0,�) = 0


Calcagni, A.E., Saueressig, ‘13ds = 2





�@� �r2

�P (x, x0,�) = 0

ds = �2@lnP (x, x,�)

@ln�= 4

�@

p� �r2

�P (x, x0,�) = 0


Calcagni, A.E., Saueressig, ‘13ds = 2

dimensional reduction: common theme in quantum gravityAmbjorn, Jurkiewicz, Loll ’05; Carlip ’09; Horava ’09….


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



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


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





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

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l

G







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







MPlanckk

g

QG-induced asymptotic safety

?QG generated fixed point


-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







MPlanckk

g

QG-induced asymptotic freedom


QG generated fixed point

?


-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

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G







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


match onto SM at Planck scale

QG generated fixed point

?


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





& 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





& 126GeV

chiral structure (light fermions) preserved[A.E., Gies ’11; Meibohm, Pawlowski ’16; A.E., Lippoldt ‘16]


!``pheno” constraint on QG[A.E., Held, Pawlowski ’16; A.E., Held ‘17]

mtop

= 176GeV





& 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


``pheno” constraint on QG[A.E., Held, Pawlowski ’16; A.E., Held ‘17]

mtop

= 176GeV


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


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]



• 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


Quantum gravity fluctuations induce

new interactions beyond MPlanck

-80 -60 -40 -20 20w2

-50

50

100βw2







�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


no photon self- interactions in the UV w/o qm gravity

-80 -60 -40 -20 20w2

-50

50

100βw2







�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)


Asymptotically safe solution to the U(1) triviality problem






�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






�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


Hints for dynamical dimensional reduction in the UV ( scale invariance)$


Matter matters for the microscopic dynamics of spacetime


10 20 30 40 50 60 70NS

10

20

30

40

ND


Standard Model matter content compatible with asymptotically safe quantum gravity


Matter matters for the microscopic dynamics of spacetime


Hints for quantum-gravity induced UV completion for the Standard Model of particle physics


• 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




[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




[ATLAS, CMS]

mh ⇡ 126GeV



[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




[ATLAS, CMS]

mh ⇡ 126GeV



[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

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