The predictive power of asymptotically safe gravity

The predictive power ofasymptotically safe gravity

Phys. Rev. Lett. 121, no. 15, 151302 (2018)Phys.Lett. B777 (2018) 217-221

Phys.Rev. D96 (2017) no.8, 086025(with Astrid Eichhorn)

and

arxiv:1904.TODAY (with Astrid Eichhorn and Roman Gold)

Quantum Gravity in ParisApril 16th 2019

Aaron HeldInstitut for Theoretical Physics, Heidelberg University

Part I:The predictive power of

asymptotic safety

Asymptotic freedom

UV

gUV

= 0

Scale invariance at a Gaussian fixed point (GFP) ensures a free (perturbatively renormalizable) UV theory

g

Asymptotic freedomcan only make

trivial predictions

Asymptotic safety

g

UV

gUV

= const

Scale invariance at a non-Gaussian fixed point (NGFP) ensures a safe (non-perturbatively renormalizable) UV theory

Asymptotic freedom

UV

gUV

= 0

Scale invariance at a Gaussian fixed point (GFP) ensures a free (perturbatively renormalizable) UV theory

g

Asymptotic safety offersUV-completions that

predict non-vanishing couplings

Asymptotic freedomcan only make

trivial predictions

Universal predictions from asymptotic safety

Irrelevant directions: Predictions from asymptotic safety

universality: consequence of a fixed point

Infrared attractive direction

non-fundamentalasymptotic safety

Free parameters of asymptotic safety

Relevant directions: Free parameters(parameterize deviation from scale invariance)

all IR values reachablefrom fixed point

Infrared repulsive direction

"

● existence of a UV fixed point for metric field theory

(fundamental theory)

Asymptotic safety conjectureWeinberg ‘76

infinite dimensional

theory space

● UV-attractive (relevant) direction: needs to be fixed by experiment● UV-repulsive (irrelevant) direction: prediction of asymptotic safety

● existence of a UV fixed point for metric field theory

(fundamental theory)

● finite number of UV-attractive directions (predictivity)

Asymptotic safety conjecture


theory space

Weinberg ‘76

● 1-loop vs 2-loop (higher loop): gauge-Yukawa models

Mechanisms for asymptotic safety

Litim, Sannino ‘14, ...


● canonical vs quantum scaling:

● Gravity in 2+ε dimensions



Weinberg ‘76Christensen, Duff ‘78

Gastmans, Kallosh, Duff ‘78...

Perturbative asymptotic safety near● quantum field with lowest interaction allowed by symmetry

● critical dimension : dimension in which marginal



● quantum fluctuations:




● asymptotically free (Landau-pole like) theories exhibit a UV-attractive (IR-attractive) fixed point above (below) the critical dimension




● asymptotically free (Landau-pole like) theories exhibit a UV-attractive (IR-attractive) fixed point above (below) the critical dimension

interactioncritical

dimensionquantum

fluctuationsinteractingfixed pointsymmetry

Yang-Mills

Wilson-Fisher

Gross-Neveu

quantum gravity

AF

LP

AF

AF

UV-FP for

IR-FP for

UV-FP for

UV-FP for

Peskin ‘80

Wilson, Fisher ‘71Brézin, Le Gillou, Zinn-Justin ‘74

Gracey ‘90Vasiliev et.Al. ‘93Rosenstein et.Al. ‘93

Hands, Kocic, Kogut ‘92 (lattice)Hofling, Novak, Wetterich ‘02 (fRG)Jannsen, Herbut ‘14 (fRG)

Gastmans, Kallosh, Truffin ‘78Christensen, Duff ‘78Kawai, Ninomiya ‘90

Canet et.Al. ‘03 (fRG)Litim, Zappala ‘10 (fRG)Hasenbusch ‘10 (latticeEichhorn, Mesterházy, Scherer ‘13 (fRG)




● Gravity in d=4








● Gravity in d=4

● competing degrees of freedom:

● fermions vs bosons: fermionic Higgs-portal

● matter vs gravity: predictive power for gauge (Yukawa) couplings


Eichhorn, Held, Vander Griend, JHEP 1808 (2018)Held, Sondenheimer ‘18




Mechanisms for asymptotic safetyfu

nct

ion

al R

eno

rmal

izat

ion

Gro

up (

fRG

)




● Gravity in d=4

● competing degrees of freedom:

● fermions vs bosons: fermionic Higgs-portal

● matter vs gravity: predictive power for gauge (Yukawa) couplings



Eichhorn, Held, Vander Griend, JHEP 1808 (2018)Held, Sondenheimer ‘18


functional RG

quantum effective action

RG-scale dependent

effective action

microscopic actionprediction of

asymptotic safety

functional RG

flow equation


asymptotic safety


RG-scale dependent

effective action

RG-scale dependent effective action

Wetterich ‘93Morris ‘94

functional RG

flow equation


asymptotic safety


RG-scale dependent

effective action



functional RG

flow equation


asymptotic safety


RG-scale dependent

effective action



functional RG

flow equation


asymptotic safety


RG-scale dependent

effective action


allows for

projectionson beta functions

projection


Asymptotic safety of quantum gravityWeinberg ‘76


theory space


theory space



theory spacetruncated


theory space

truncated





theory space

truncated fixedpoint

symmetry invariants

☑

☑

☒

☒ ☒

☑ ☒

Benedetti, Machado, Saueressig ‘09

Reuter ‘96

☑

☑

☑

☒

☒

...

...

☒

...

Codello, Percacci, Rahmede ’07, ’08Machado, Saueressig ‘07

K. Falls et.Al ‘13K. Falls et.Al ‘18

Reuter, Lauscher ‘02

Gies, Knorr, Lippoldt, Saueressig ‘16


MPlanck

Mew

canonical scaling

Codello, Percacci, Rahmede ‘08

quantumfluctuations

canonicalscaling

Asymptotic safety

: dimfull

: dimless

fixed-point scaling




theory space

truncated fixedpoint

symmetry invariants

☑

☑

☒

☒ ☒

☑ ☒


Reuter ‘96

☑

☑

☑

☒

☒

...

...

☒

...






MPlanck

Mew

canonical scaling


quantumfluctuations

canonicalscaling

Asymptotic safety

: dimfull

: dimless

fixed-point scaling

predictedcouplings

freeparameters

Planckscale

electroweakscale

ob

serv

able

s

fixedpoint

symmetry invariants

☑

☑

☒

☒ ☒

☑ ☒


Reuter ‘96

☑

☑

☑

☒

☒

...

...

☒

...





Asymptotic safety of quantum gravity

MPlanck

Mew

canonical scaling


quantumfluctuations

canonicalscaling

Asymptotic safety

: dimfull

: dimless

fixed-point scaling

predictedcouplings

freeparameters

Standard Model 1-loop running, cf. Buttazzo et.Al. ‘13

electroweakscale

Planckscale

ob

serv

able

s

fixedpoint

symmetry invariants

☑

☑

☒

☒ ☒

☑ ☒


Reuter ‘96

☑

☑

☑

☒

☒

...

...

☒

...





Weinberg ‘76


MPlanck

Mew

canonical scaling


quantumfluctuations

canonicalscaling

Asymptotic safety

: dimfull

: dimless

fixed-point scaling

fixedpoint

symmetry invariants

☑

☑

☒

☒ ☒

☑ ☒


Reuter ‘96

predictedcouplings

freeparameters


electroweakscale

Planckscale

ob

serv

able

s

desert

☑

☑

☑

☒

☒

...

...

☒

...





Weinberg ‘76


MPlanck

Mew

canonical scaling


quantumfluctuations

canonicalscaling

Asymptotic safety

: dimfull

: dimless

fixed-point scaling

predictedcouplings

freeparameters


electroweakscale

Planckscale

ob

serv

able

s

desert

no-desert:bSM scenarios

Christiansen, Eichhorn, AH, PRD 96 (2017)Eichhorn, AH, Wetterich, PLB 782 (2018)

Eichhorn, AH, Vander Griend, JHEP 1808 (2018)

fixedpoint

symmetry invariants

☑

☑

☒

☒ ☒

☑ ☒


Reuter ‘96

☑

☑

☑

☒

☒

...

...

☒

...





Weinberg ‘76

Major open questions (my selection)

Theoretical consistency Phenomenological viability

● AS & unitarity

● Lorentzian signature

● Background independence

● Full momentum dependence & scheme dependence

Benedetti, Machado, Saueressig ‘09Becker, Ripken, Saueressig ‘17Arici, Becker, Ripken, Saueressig, Suijlekom ‘17...

Pawlowski, Donkin ‘12Becker, Reuter ‘14Morris ‘16Percacci, Vacca ‘16Ohta ‘16

Manrique, Rechenberger, Saueressig ‘11

Causal Set RG /Tensor Model RGEichhorn, Koslowski ‘13, ‘14, ‘17Eichhorn, Lumma, Koslowski, Pereira ‘18Eichhorn, Koslowski, Pereira ‘18

Eichhorn ‘17, ‘19

Christiansen, Pawlowski, Rodigast ‘14Gies, Knorr, Lippoldt ‘15Christiansen, Knorr, Meibohm, Pawlowski, Reichert ‘15Denz, Pawlowski, Reichert ‘16Knorr, Lippoldt ‘17...

● Implications for cosmology

● Link to Particle Physics

● Black Holes and Strong Gravity

Bonanno, Contillo, Percacci ‘10Bonenno, Platania ‘15Wetterich ‘17Bonanno, Platania, Saueressig ‘18...

Wetterich, Shaposhnikov ‘09 Daum, Harst, Reuter ‘10 Eichhorn, Held ‘17, ‘17, ‘18Eichhorn, Versteegen ‘17...

Bonanno, Reuter ‘98, ‘00Falls, Litim ‘12Contreras, Koch, Rioseco ‘13Koch, Saueressig ‘13Pawlowski, Stock ‘18Adeifeoba, Eichhorn, Platania ‘18Platania ‘19Held, Gold, Eichhorn ‘19...

Major open questions (my selection)

Theoretical consistency Phenomenological viability

● AS & unitarity

● Lorentzian signature

● Background independence

● Full momentum dependence & scheme dependence

Benedetti, Machado, Saueressig ‘09Becker, Ripken, Saueressig ‘17Arici, Becker, Ripken, Saueressig, Suijlekom ‘17...

Pawlowski, Donkin ‘12Becker, Reuter ‘14Morris ‘16Percacci, Vacca ‘16Ohta ‘16

Manrique, Rechenberger, Saueressig ‘11

Causal Set RG /Tensor Model RGEichhorn, Koslowski ‘13, ‘14, ‘17Eichhorn, Lumma, Koslowski, Pereira ‘18Eichhorn, Koslowski, Pereira ‘18

Eichhorn ‘17, ‘19

Christiansen, Pawlowski, Rodigast ‘14Gies, Knorr, Lippoldt ‘15Christiansen, Knorr, Meibohm, Pawlowski, Reichert ‘15Denz, Pawlowski, Reichert ‘16Knorr, Lippoldt ‘17...

● Implications for cosmology

● Link to Particle Physics

● Black Holes and Strong Gravity

Bonanno, Contillo, Percacci ‘10Bonenno, Platania ‘15Wetterich ‘17Bonanno, Platania, Saueressig ‘18...

Wetterich, Shaposhnikov ‘09 Daum, Harst, Reuter ‘10 Eichhorn, Held ‘17, ‘17, ‘18Eichhorn, Versteegen ‘17...

Bonanno, Reuter ‘98, ‘00Falls, Litim ‘12Contreras, Koch, Rioseco ‘13Koch, Saueressig ‘13Pawlowski, Stock ‘18Adeifeoba, Eichhorn, Platania ‘18Platania ‘19Held, Gold, Eichhorn ‘19...

Part II:The status of asymptotically safe

gravity and matter

Eichhorn, Held ‘18

Persistence of a gravitational scaling regime

scale-invariantregime

Reuter, Saueressig ‘01

● Gravitational scaling regime persists when Standard Model matter is included

no matter with SM matter: NV=12, N

S=4, N

W=45

Donà, Eichhorn, Percacci ‘13Meibohm, Pawlowski, Reichert ‘16Biemans, Platania, Saueressig ‘17

Christiansen, Litim, Pawlowski, Reichert ‘17






S=4, N

W=45



simplified form: Donà, Eichhorn, Percacci ‘13

● fermionic matter tends toshift gravity to large negative Λ

background-field approximation







S=4, N

W=45




● generically suppresses contributions to matterbecause Λ acts as an effective mass

Donà, Eichhorn, Percacci ‘13background-field approximation

Newton coupling

cosmologicalconstant

higher curvature







S=4, N

W=45




● generically suppresses contributions to matterbecause Λ acts as an effective mass

Donà, Eichhorn, Percacci ‘13background-field approximation

● no complete SM-study yet● no such suppression observed

fluctuating fieldsMeibohm, Pawlowski, Reichert ‘16


Newton coupling

cosmologicalconstant

higher curvature

Standard Model fluctuations

quantum gravityfluctuations

Constraints from & Consistency with Standard Model physics

Standard Model fluctuations

quantum gravityfluctuations

non-Abelian g2,3

:

fixed pointasymptotically safe

phenomenologyparameters

of the SM

Higgs quartic λ4 :

U(1) gauge g1 :

Yukawas yt,b

:


non-Abelian g2,3

:



of the SM

Higgs quartic λ4 :

U(1) gauge g1 :

Yukawas yt,b

:

antiscreeningRobinson, Wilczek, ‘06Daum, Harst, Reuter, ‘10Folkerts, Litim, Pawlowski, ‘12Christiansen, Eichhorn, ‘17Christiansen, Litim, Pawlowski, Reichert, ‘17

antiscreening

antiscreening

antiscreening


antiscreening

non-Abelian gauge couplings

antiscreening

● Reinforces asymptotic freedom

● Non-Abelian gauge couplings remain free parameters

non-Abelian g2,3

: antiscreening reinforcesasymptotic

freedom

Robinson, Wilczek, ‘06Daum, Harst, Reuter, ‘10Folkerts, Litim, Pawlowski, ‘12Christiansen, Eichhorn, ‘17Christiansen, Litim, Pawlowski, Reichert, ‘17

antiscreening



of the SM

Higgs quartic λ4 :

U(1) gauge g1 :

Yukawas yt,b

:

antiscreening

antiscreening


non-Abelian g2,3


freedom


antiscreening

fixed point

screening screening

asymptotically safephenomenology

parametersof the SM

Higgs quartic λ4 :

U(1) gauge g1 :

Yukawas yt,b

:

screening

screening

Griguolo, Percacci ‘95Percacci, Perini ‘03Narain, Percacci ‘09


screening

Quartic Higgs coupling

● quartic couplings IR-attractive at transplanckian scales (predictive)

MH

≈ 129 GeVShaposhnikov, Wetterich, ‘09

Griguolo, Percacci ‘95Percacci, Perini ‘03Narain, Percacci ‘09screening

Moch, Reuter, ‘18

non-Abelian g2,3


freedom


antiscreening

fixed point

screening screeningShaposhnikov, Wetterich, ‘09


parametersof the SM

Higgs quartic λ4 :

U(1) gauge g1 :

Yukawas yt,b

:

screening

screening


MH

≈ 129 GeV


non-Abelian g2,3


freedom

Harst, Reuter, ‘11Eichhorn, Versteegen ‘17


screening

antiscreening

screeningShaposhnikov, Wetterich, ‘09

screening antiscreening



of the SM

Higgs quartic λ4 :

U(1) gauge g1 :

Yukawas yt,b

:


antiscreening

screening


MH

≈ 129 GeV

antiscreening

screening

running of the couplingbeta-function

free UV-repulsive FP

triviality problem

Asymptotically safe abelian gauge coupling

antiscreening

screening



interacting UV-repulsive FP


antiscreening

screening


Eichhorn, Versteegen ‘17




antiscreening


screening





● interacting fixed point uniquely fixes fine-structure constant

● UV-completion demands upper bound gY,IR

0.47 (g⪅Y,exp

=0.355)

Eichhorn, Versteegen ‘17Eichhorn, Held, Wetterich ‘17

Eichhorn, Versteegen ‘17 e.g. Buttazzo et.Al, ‘13

non-Abelian g2,3


freedom



screening

antiscreening

screening

gY

0.47⪅

Shaposhnikov, Wetterich, ‘09

Eichhorn, Versteegen ‘17screening antiscreening



of the SM

Higgs quartic λ4 :

U(1) gauge g1 :

Yukawas yt,b

:


antiscreening

screening


MH

≈ 129 GeV

non-Abelian g2,3

: antiscreening


reinforcesasymptotic

freedom


Robinson, Wilczek, ‘06Daum, Harst, Reuter, ‘10Folkerts, Litim, Pawlowski, ‘12Christiansen, Eichhorn, ‘17Christiansen, Litim, Pawlowski, Reichert ‘17

Higgs quartic λ4 :

U(1) gauge g1 :

Yukawas yt,b

:

screening

antiscreening

screening

gY

0.47⪅



Zanusso, Vacca, Percacci, Zambelli,’10Oda, Yamada, ‘16Eichhorn, Held, Pawlowski, ‘16Eichhorn, Held, ‘17

screening

screening

antiscreening

antiscreening

fixed pointparameters

of the SM


antiscreening

screening


MH

≈ 129 GeV

Asymptotically safe Yukawa couplings

antiscreening

screening

Eichhorn, Held ‘17, 1707.01107


free UV-attractive FP


perturbatively small


antiscreening

screening

perturbatively smallOda, Yamada, ‘16Eichhorn, Held, Pawlowski, ‘16Eichhorn, Held, ‘17

Eichhorn and Held ‘17Eichhorn, Held and Pawlowski ‘16Christiansen & Eichhorn, 2017


antiscreening

screening

minimally coupled matter


NV=12, N

S=4, N

W=0

no fermion family



antiscreening

screening



NV=12, N

S=4, N

W=15

1 fermion family



antiscreening

screening



NV=12, N

S=4, N

W=30

2 fermion family



antiscreening

screening



NV=12, N

S=4, N

W=45

3 fermion family

● Gravitational scaling regime persists with minimally coupled Standard Model

● fermionic matter leads to fy > 0

● generically leads to perturbative regime asΛ acts as an effective mass




antiscreening

screening




asymptotic safety

within a simple truncationEichhorn, Held ‘17


non-Abelian g2,3

: antiscreening


reinforcesasymptotic

freedom


Robinson, Wilczek, ‘06Daum, Harst, Reuter, ‘10Folkerts, Litim, Pawlowski, ‘12Christiansen, Eichhorn, ‘17Christiansen, Litim, Pawlowski, Reichert ‘17

Higgs quartic λ4 :

U(1) gauge g1 :

Yukawas yt,b

:

screening

antiscreening

screening

Mt

170 GeV⪅

gY

0.47⪅



Eichhorn, Held ‘17Zanusso, Vacca, Percacci, Zambelli,’10Oda, Yamada, ‘16Eichhorn, Held, Pawlowski, ‘16Eichhorn, Held, ‘17

screening

screening

antiscreening

antiscreening

fixed pointparameters

of the SM


antiscreening

screening


MH

≈ 129 GeV

Mass difference for charged quarks

● desert: no new physics at intermediate scales

● UV scaling-regime for quantum gravity (asymptotic safety)

● leading order quantum-gravity effects can be parametrized in

assume:


mass differencefrom

charge difference

Mass difference for charged quarksScale dependence most predictive fixed point


Scale dependence most predictive fixed point
















How non-trivial is this relation?


● Links quantum numbers (charges) of top and bottom to their mass difference

How non-trivial is this relation?



● Hints towards a universal force (quantum gravity)

How non-trivial is this relation?● Links quantum

numbers (charges) of top and bottom to their mass difference



● Hints towards a universal force (quantum gravity)

● points towards the Planck scale (quantum gravity)

How non-trivial is this relation?● Links quantum

numbers (charges) of top and bottom to their mass difference




● Potentially higher predictive power than the Standard Model

● Standard Model couplings at electroweak scale could constrain Planck-scale physics

● effectively perturbative regime relies on mass-like suppression of gravitational fluctuations

… in a nutshell

Part III:Asymptotic safety casts its shadow

Regular spherical spacetime● Singularities: GR predicts its own breakdown


MPlanck

Mew

canonical scaling


quantumfluctuations

canonicalscaling

: dimfull

: dimless

fixed-point scaling


MPlanck

Mew

canonical scaling


quantumfluctuations

canonicalscaling

: dimfull

: dimless

fixed-point scaling

● Dim’less running Newton coupling


MPlanck

Mew

canonical scaling


quantumfluctuations

canonicalscaling

: dimfull

: dimless

fixed-point scaling


● RG-scale identification with curvature


MPlanck

Mew

canonical scaling


quantumfluctuations

canonicalscaling

: dimfull

: dimless

fixed-point scaling



Reuter, Bonanno ‘99, ‘00, ...

Regular axisymmetric spacetime● Singularities: GR predicts its own breakdown






qualitatively the same:enveloping function

proper distance of infalling observer




HorizonHorizon

Held, Gold, Eichhorn ‘19

qualitatively the same:enveloping function

proper distance of infalling observer

Where to expect effects?

Planckiansingularity resolution

non-Planckiansingularity resolution

Planckian BHs astrophysical BHs

✔✔ ✔

✘





✔✔ ✔

✘

a = 0.3, 0.6, 0.9, 0.99 rg





Younsi et. Al ‘16

retrograde(against frame dragging)

✔✔ ✔

✘

a = 0.3, 0.6, 0.9, 0.99 rg





✔✔ ✔

✘

a = 0.3, 0.6, 0.9, 0.99 rg





✔✔ ✔

prograde(frame dragged)

probes horizon scales

✘

a = 0.3, 0.6, 0.9, 0.99 rg

No degeneracy in the shadow

● Spherically symmetric BHs could be distinguished byweak-field vs. strong-field

mass measurementsAbuter et al. ‘19 EHT-collaboration ‘19

No degeneracy in the shadow

● Spherically symmetric BHs could be distinguished byweak-field vs. strong-field

mass measurements

● Strongly spinning BHs are very sensitive to horizon-scale modifications

Held, Gold, Eichhorn ‘19

Abuter et al. ‘19 EHT-collaboration ‘19

a = 0.9 rg

Generic result of (QG) singularity resolution?

Dymnikova ‘92, ‘96Hayward ‘06

...

Singularity-resolving spacetimes with deSitter core


...


Gambini, Pullin ‘08, ‘13

Modesto ‘10

Rovelli, Vidotto ‘14

Loop Quantum Gravity



...



Modesto ‘10



Nicolini, Spallucci,Wondrak ‘19,...

Stringy Theory



...



Modesto ‘10



Nicolini, Spallucci,Wondrak ‘19,...

Stringy Theory

Noncommutative spacetime structure

Nicolini, Smailagic,Spallucci ‘05


Kerr (GR)

Kerr (regular / quantum)

– Thank you for your attention. –

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The predictive power of asymptotically safe gravity