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)

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

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

Asymptotic freedomcan only make

trivial predictions

Asymptotic safety

= const

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

Asymptotic freedom

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

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

interactioncritical

dimensionquantum

fluctuationsinteractingfixed pointsymmetry

Yang-Mills

Wilson-Fisher

Gross-Neveu

quantum gravity

UV-FP for

IR-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

● 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

● 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 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

canonical scaling

Codello, Percacci, Rahmede ‘08

quantumfluctuations

canonicalscaling

Asymptotic safety

: dimfull

: dimless

fixed-point scaling

theory space

truncated fixedpoint

symmetry invariants

☒ ☒

☑ ☒

Reuter ‘96

MPlanck

canonical scaling

quantumfluctuations

canonicalscaling

Asymptotic safety

: dimfull

: dimless

fixed-point scaling

predictedcouplings

freeparameters

Planckscale

electroweakscale

fixedpoint

symmetry invariants

☒ ☒

☑ ☒

Reuter ‘96

Asymptotic safety of quantum gravity

MPlanck

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

fixedpoint

symmetry invariants

☒ ☒

☑ ☒

Reuter ‘96

Weinberg ‘76

MPlanck

canonical scaling

quantumfluctuations

canonicalscaling

Asymptotic safety

: dimfull

: dimless

fixed-point scaling

fixedpoint

symmetry invariants

☒ ☒

☑ ☒

Reuter ‘96

predictedcouplings

freeparameters

electroweakscale

Planckscale

desert

Weinberg ‘76

MPlanck

canonical scaling

quantumfluctuations

canonicalscaling

Asymptotic safety

: dimfull

: dimless

fixed-point scaling

predictedcouplings

freeparameters

electroweakscale

Planckscale

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

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

Christiansen, Litim, Pawlowski, Reichert ‘17

S=4, N

simplified form: Donà, Eichhorn, Percacci ‘13

● fermionic matter tends toshift gravity to large negative Λ

background-field approximation

S=4, N

● 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

● 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

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

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

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

screening

Quartic Higgs coupling

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

≈ 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

≈ 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

≈ 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

0.47⪅

Shaposhnikov, Wetterich, ‘09

Eichhorn, Versteegen ‘17screening antiscreening

of the SM

Higgs quartic λ4 :

U(1) gauge g1 :

Yukawas yt,b

antiscreening

screening

≈ 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

0.47⪅

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

screening

antiscreening

fixed pointparameters

of the SM

antiscreening

screening

≈ 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

no fermion family

antiscreening

screening

NV=12, N

S=4, N

1 fermion family

antiscreening

screening

NV=12, N

S=4, N

2 fermion family

antiscreening

screening

NV=12, N

S=4, N

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

170 GeV⪅

0.47⪅

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

screening

antiscreening

fixed pointparameters

of the SM

antiscreening

screening

≈ 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

canonical scaling

quantumfluctuations

canonicalscaling

: dimfull

: dimless

fixed-point scaling

MPlanck

canonical scaling

quantumfluctuations

canonicalscaling

: dimfull

: dimless

fixed-point scaling

● Dim’less running Newton coupling

MPlanck

canonical scaling

quantumfluctuations

canonicalscaling

: dimfull

: dimless

fixed-point scaling

● RG-scale identification with curvature

MPlanck

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. –

the predictive power of asymptotically safe gravity

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