the predictive power of asymptotically safe gravity
TRANSCRIPT
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
infinite dimensional
theory space
Weinberg ‘76
● 1-loop vs 2-loop (higher loop): gauge-Yukawa models
Mechanisms for asymptotic safety
Litim, Sannino ‘14, ...
● 1-loop vs 2-loop (higher loop): gauge-Yukawa models
● canonical vs quantum scaling:
● Gravity in 2+ε dimensions
Mechanisms for asymptotic safety
Litim, Sannino ‘14, ...
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
Perturbative asymptotic safety near● quantum field with lowest interaction allowed by symmetry
● critical dimension : dimension in which marginal
● quantum fluctuations:
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
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
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)
● 1-loop vs 2-loop (higher loop): gauge-Yukawa models
● canonical vs quantum scaling:
● Gravity in 2+ε dimensions
● Gravity in d=4
Mechanisms for asymptotic safety
Litim, Sannino ‘14, ...
Weinberg ‘76Christensen, Duff ‘78
Gastmans, Kallosh, Duff ‘78...
● 1-loop vs 2-loop (higher loop): gauge-Yukawa models
● canonical vs quantum scaling:
● Gravity in 2+ε dimensions
● Gravity in d=4
● competing degrees of freedom:
● fermions vs bosons: fermionic Higgs-portal
● matter vs gravity: predictive power for gauge (Yukawa) couplings
Mechanisms for asymptotic safety
Eichhorn, Held, Vander Griend, JHEP 1808 (2018)Held, Sondenheimer ‘18
Litim, Sannino ‘14, ...
Weinberg ‘76Christensen, Duff ‘78
Gastmans, Kallosh, Duff ‘78...
Mechanisms for asymptotic safetyfu
nct
ion
al R
eno
rmal
izat
ion
Gro
up (
fRG
)
● 1-loop vs 2-loop (higher loop): gauge-Yukawa models
● canonical vs quantum scaling:
● Gravity in 2+ε dimensions
● Gravity in d=4
● competing degrees of freedom:
● fermions vs bosons: fermionic Higgs-portal
● matter vs gravity: predictive power for gauge (Yukawa) couplings
Weinberg ‘76Christensen, Duff ‘78
Gastmans, Kallosh, Duff ‘78...
Eichhorn, Held, Vander Griend, JHEP 1808 (2018)Held, Sondenheimer ‘18
Litim, Sannino ‘14, ...
functional RG
quantum effective action
RG-scale dependent
effective action
microscopic actionprediction of
asymptotic safety
functional RG
flow equation
microscopic actionprediction of
asymptotic safety
quantum effective action
RG-scale dependent
effective action
RG-scale dependent effective action
Wetterich ‘93Morris ‘94
functional RG
flow equation
microscopic actionprediction of
asymptotic safety
quantum effective action
RG-scale dependent
effective action
RG-scale dependent effective action
Wetterich ‘93Morris ‘94
functional RG
flow equation
microscopic actionprediction of
asymptotic safety
quantum effective action
RG-scale dependent
effective action
RG-scale dependent effective action
Wetterich ‘93Morris ‘94
functional RG
flow equation
microscopic actionprediction of
asymptotic safety
quantum effective action
RG-scale dependent
effective action
RG-scale dependent effective action
allows for
projectionson beta functions
projection
Wetterich ‘93Morris ‘94
Asymptotic safety of quantum gravityWeinberg ‘76
infinite dimensional
theory space
infinite dimensional
theory space
Asymptotic safety of quantum gravityWeinberg ‘76
infinite dimensional
theory spacetruncated
infinite dimensional
theory space
truncated
Asymptotic safety of quantum gravityWeinberg ‘76
infinite dimensional
theory spacetruncated
infinite dimensional
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
Asymptotic safety of quantum gravityWeinberg ‘76
MPlanck
Mew
canonical scaling
Codello, Percacci, Rahmede ‘08
quantumfluctuations
canonicalscaling
Asymptotic safety
: dimfull
: dimless
fixed-point scaling
infinite dimensional
theory spacetruncated
infinite dimensional
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
Asymptotic safety of quantum gravityWeinberg ‘76
MPlanck
Mew
canonical scaling
Codello, Percacci, Rahmede ‘08
quantumfluctuations
canonicalscaling
Asymptotic safety
: dimfull
: dimless
fixed-point scaling
predictedcouplings
freeparameters
Planckscale
electroweakscale
ob
serv
able
s
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
Asymptotic safety of quantum gravity
MPlanck
Mew
canonical scaling
Codello, Percacci, Rahmede ‘08
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
☑
☑
☒
☒ ☒
☑ ☒
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
Weinberg ‘76
Asymptotic safety of quantum gravity
MPlanck
Mew
canonical scaling
Codello, Percacci, Rahmede ‘08
quantumfluctuations
canonicalscaling
Asymptotic safety
: dimfull
: dimless
fixed-point scaling
fixedpoint
symmetry invariants
☑
☑
☒
☒ ☒
☑ ☒
Benedetti, Machado, Saueressig ‘09
Reuter ‘96
predictedcouplings
freeparameters
Standard Model 1-loop running, cf. Buttazzo et.Al. ‘13
electroweakscale
Planckscale
ob
serv
able
s
desert
☑
☑
☑
☒
☒
...
...
☒
...
Codello, Percacci, Rahmede ’07, ’08Machado, Saueressig ‘07
K. Falls et.Al ‘13K. Falls et.Al ‘18
Reuter, Lauscher ‘02
Gies, Knorr, Lippoldt, Saueressig ‘16
Weinberg ‘76
Asymptotic safety of quantum gravity
MPlanck
Mew
canonical scaling
Codello, Percacci, Rahmede ‘08
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
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
☑
☑
☒
☒ ☒
☑ ☒
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
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
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
simplified form: Donà, Eichhorn, Percacci ‘13
● fermionic matter tends toshift gravity to large negative Λ
background-field approximation
Persistence of a gravitational scaling regime
scale-invariantregime
Reuter, Saueressig ‘01
● Gravitational scaling regime persists when Standard Model matter is included
simplified form: Donà, Eichhorn, Percacci ‘13
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
● fermionic matter tends toshift gravity to large negative Λ
● generically suppresses contributions to matterbecause Λ acts as an effective mass
Donà, Eichhorn, Percacci ‘13background-field approximation
Newton coupling
cosmologicalconstant
higher curvature
Persistence of a gravitational scaling regime
scale-invariantregime
Reuter, Saueressig ‘01
● Gravitational scaling regime persists when Standard Model matter is included
simplified form: Donà, Eichhorn, Percacci ‘13
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
● fermionic matter tends toshift gravity to large negative Λ
● 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
Christiansen, Litim, Pawlowski, Reichert ‘17
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
:
Constraints from & Consistency with Standard Model physics
non-Abelian g2,3
:
fixed pointasymptotically safe
phenomenologyparameters
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
Constraints from & Consistency with Standard Model physics
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
fixed pointasymptotically safe
phenomenologyparameters
of the SM
Higgs quartic λ4 :
U(1) gauge g1 :
Yukawas yt,b
:
antiscreening
antiscreening
Constraints from & Consistency with Standard Model physics
non-Abelian g2,3
: antiscreening reinforcesasymptotic
freedom
Robinson, Wilczek, ‘06Daum, Harst, Reuter, ‘10Folkerts, Litim, Pawlowski, ‘12Christiansen, Eichhorn, ‘17Christiansen, Litim, Pawlowski, Reichert, ‘17
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
Constraints from & Consistency with Standard Model physics
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
: antiscreening reinforcesasymptotic
freedom
Robinson, Wilczek, ‘06Daum, Harst, Reuter, ‘10Folkerts, Litim, Pawlowski, ‘12Christiansen, Eichhorn, ‘17Christiansen, Litim, Pawlowski, Reichert, ‘17
antiscreening
fixed point
screening screeningShaposhnikov, Wetterich, ‘09
asymptotically safephenomenology
parametersof the SM
Higgs quartic λ4 :
U(1) gauge g1 :
Yukawas yt,b
:
screening
screening
Griguolo, Percacci ‘95Percacci, Perini ‘03Narain, Percacci ‘09
MH
≈ 129 GeV
Constraints from & Consistency with Standard Model physics
non-Abelian g2,3
: antiscreening reinforcesasymptotic
freedom
Harst, Reuter, ‘11Eichhorn, Versteegen ‘17
Robinson, Wilczek, ‘06Daum, Harst, Reuter, ‘10Folkerts, Litim, Pawlowski, ‘12Christiansen, Eichhorn, ‘17Christiansen, Litim, Pawlowski, Reichert, ‘17
screening
antiscreening
screeningShaposhnikov, Wetterich, ‘09
screening antiscreening
fixed pointasymptotically safe
phenomenologyparameters
of the SM
Higgs quartic λ4 :
U(1) gauge g1 :
Yukawas yt,b
:
Griguolo, Percacci ‘95Percacci, Perini ‘03Narain, Percacci ‘09
antiscreening
screening
Constraints from & Consistency with Standard Model physics
MH
≈ 129 GeV
antiscreening
screening
running of the couplingbeta-function
free UV-repulsive FP
triviality problem
Asymptotically safe abelian gauge coupling
antiscreening
screening
running of the couplingbeta-function
free UV-repulsive FP
interacting UV-repulsive FP
Asymptotically safe abelian gauge coupling
antiscreening
screening
running of the couplingbeta-function
Eichhorn, Versteegen ‘17
free UV-repulsive FP
interacting UV-repulsive FP
Asymptotically safe abelian gauge coupling
antiscreening
Asymptotically safe abelian gauge coupling
screening
running of the couplingbeta-function
Eichhorn, Versteegen ‘17
free UV-repulsive FP
interacting UV-repulsive FP
● 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
: antiscreening reinforcesasymptotic
freedom
Harst, Reuter, ‘11Eichhorn, Versteegen ‘17
Robinson, Wilczek, ‘06Daum, Harst, Reuter, ‘10Folkerts, Litim, Pawlowski, ‘12Christiansen, Eichhorn, ‘17Christiansen, Litim, Pawlowski, Reichert, ‘17
screening
antiscreening
screening
gY
0.47⪅
Shaposhnikov, Wetterich, ‘09
Eichhorn, Versteegen ‘17screening antiscreening
fixed pointasymptotically safe
phenomenologyparameters
of the SM
Higgs quartic λ4 :
U(1) gauge g1 :
Yukawas yt,b
:
Griguolo, Percacci ‘95Percacci, Perini ‘03Narain, Percacci ‘09
antiscreening
screening
Constraints from & Consistency with Standard Model physics
MH
≈ 129 GeV
non-Abelian g2,3
: antiscreening
asymptotically safephenomenology
reinforcesasymptotic
freedom
Harst, Reuter, ‘11Eichhorn, Versteegen ‘17
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⪅
Shaposhnikov, Wetterich, ‘09
Eichhorn, Versteegen ‘17
Zanusso, Vacca, Percacci, Zambelli,’10Oda, Yamada, ‘16Eichhorn, Held, Pawlowski, ‘16Eichhorn, Held, ‘17
screening
screening
antiscreening
antiscreening
fixed pointparameters
of the SM
Griguolo, Percacci ‘95Percacci, Perini ‘03Narain, Percacci ‘09
antiscreening
screening
Constraints from & Consistency with Standard Model physics
MH
≈ 129 GeV
Asymptotically safe Yukawa couplings
antiscreening
screening
Eichhorn, Held ‘17, 1707.01107
running of the couplingbeta-function
free UV-attractive FP
interacting UV-repulsive FP
perturbatively small
Asymptotically safe Yukawa couplings
antiscreening
screening
perturbatively smallOda, Yamada, ‘16Eichhorn, Held, Pawlowski, ‘16Eichhorn, Held, ‘17
Eichhorn and Held ‘17Eichhorn, Held and Pawlowski ‘16Christiansen & Eichhorn, 2017
Asymptotically safe Yukawa couplings
antiscreening
screening
minimally coupled matter
simplified form: Donà, Eichhorn, Percacci ‘13
NV=12, N
S=4, N
W=0
no fermion family
perturbatively smallOda, Yamada, ‘16Eichhorn, Held, Pawlowski, ‘16Eichhorn, Held, ‘17
Asymptotically safe Yukawa couplings
antiscreening
screening
minimally coupled matter
simplified form: Donà, Eichhorn, Percacci ‘13
NV=12, N
S=4, N
W=15
1 fermion family
perturbatively smallOda, Yamada, ‘16Eichhorn, Held, Pawlowski, ‘16Eichhorn, Held, ‘17
Asymptotically safe Yukawa couplings
antiscreening
screening
minimally coupled matter
simplified form: Donà, Eichhorn, Percacci ‘13
NV=12, N
S=4, N
W=30
2 fermion family
perturbatively smallOda, Yamada, ‘16Eichhorn, Held, Pawlowski, ‘16Eichhorn, Held, ‘17
Asymptotically safe Yukawa couplings
antiscreening
screening
minimally coupled matter
simplified form: Donà, Eichhorn, Percacci ‘13
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
Donà, Eichhorn, Percacci ‘13Meibohm, Pawlowski, Reichert ‘16Biemans, Platania, Saueressig ‘17
perturbatively smallOda, Yamada, ‘16Eichhorn, Held, Pawlowski, ‘16Eichhorn, Held, ‘17
Asymptotically safe Yukawa couplings
antiscreening
screening
minimally coupled matter
simplified form: Donà, Eichhorn, Percacci ‘13
Eichhorn, Held ‘17
asymptotic safety
within a simple truncationEichhorn, Held ‘17
perturbatively smallOda, Yamada, ‘16Eichhorn, Held, Pawlowski, ‘16Eichhorn, Held, ‘17
non-Abelian g2,3
: antiscreening
asymptotically safephenomenology
reinforcesasymptotic
freedom
Harst, Reuter, ‘11Eichhorn, Versteegen ‘17
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⪅
Shaposhnikov, Wetterich, ‘09
Eichhorn, Versteegen ‘17
Eichhorn, Held ‘17Zanusso, Vacca, Percacci, Zambelli,’10Oda, Yamada, ‘16Eichhorn, Held, Pawlowski, ‘16Eichhorn, Held, ‘17
screening
screening
antiscreening
antiscreening
fixed pointparameters
of the SM
Griguolo, Percacci ‘95Percacci, Perini ‘03Narain, Percacci ‘09
antiscreening
screening
Constraints from & Consistency with Standard Model physics
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:
Eichhorn, Held ‘18
mass differencefrom
charge difference
Mass difference for charged quarksScale dependence most predictive fixed point
Eichhorn, Held ‘18
Scale dependence most predictive fixed point
Mass difference for charged quarks
Eichhorn, Held ‘18
Scale dependence most predictive fixed point
Mass difference for charged quarks
Eichhorn, Held ‘18
Scale dependence most predictive fixed point
Mass difference for charged quarks
Eichhorn, Held ‘18
Scale dependence most predictive fixed point
Mass difference for charged quarks
Eichhorn, Held ‘18
Scale dependence most predictive fixed point
Mass difference for charged quarks
Eichhorn, Held ‘18
Scale dependence most predictive fixed point
How non-trivial is this relation?
Eichhorn, Held ‘18
● Links quantum numbers (charges) of top and bottom to their mass difference
How non-trivial is this relation?
Eichhorn, Held ‘18
Eichhorn, Held ‘18
● 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
Eichhorn, Held ‘18
Eichhorn, Held ‘18
● 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
Eichhorn, Held ‘18
Eichhorn, Held ‘18
Eichhorn, Held ‘18
● 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
Regular spherical spacetime● Singularities: GR predicts its own breakdown
MPlanck
Mew
canonical scaling
Codello, Percacci, Rahmede ‘08
quantumfluctuations
canonicalscaling
: dimfull
: dimless
fixed-point scaling
Regular spherical spacetime● Singularities: GR predicts its own breakdown
MPlanck
Mew
canonical scaling
Codello, Percacci, Rahmede ‘08
quantumfluctuations
canonicalscaling
: dimfull
: dimless
fixed-point scaling
● Dim’less running Newton coupling
Regular spherical spacetime● Singularities: GR predicts its own breakdown
MPlanck
Mew
canonical scaling
Codello, Percacci, Rahmede ‘08
quantumfluctuations
canonicalscaling
: dimfull
: dimless
fixed-point scaling
● Dim’less running Newton coupling
● RG-scale identification with curvature
Regular spherical spacetime● Singularities: GR predicts its own breakdown
MPlanck
Mew
canonical scaling
Codello, Percacci, Rahmede ‘08
quantumfluctuations
canonicalscaling
: dimfull
: dimless
fixed-point scaling
● Dim’less running Newton coupling
● RG-scale identification with curvature
Reuter, Bonanno ‘99, ‘00, ...
Regular axisymmetric spacetime● Singularities: GR predicts its own breakdown
● Dim’less running Newton coupling
● RG-scale identification with curvature
Regular axisymmetric spacetime● Singularities: GR predicts its own breakdown
● Dim’less running Newton coupling
● RG-scale identification with curvature
qualitatively the same:enveloping function
proper distance of infalling observer
Regular axisymmetric spacetime● Singularities: GR predicts its own breakdown
● Dim’less running Newton coupling
● RG-scale identification with curvature
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
✔✔ ✔
✘
Where to expect effects?
Planckiansingularity resolution
non-Planckiansingularity resolution
Planckian BHs astrophysical BHs
✔✔ ✔
✘
a = 0.3, 0.6, 0.9, 0.99 rg
Where to expect effects?
Planckiansingularity resolution
non-Planckiansingularity resolution
Planckian BHs astrophysical BHs
Younsi et. Al ‘16
retrograde(against frame dragging)
✔✔ ✔
✘
a = 0.3, 0.6, 0.9, 0.99 rg
Where to expect effects?
Planckiansingularity resolution
non-Planckiansingularity resolution
Planckian BHs astrophysical BHs
✔✔ ✔
✘
a = 0.3, 0.6, 0.9, 0.99 rg
Where to expect effects?
Planckiansingularity resolution
non-Planckiansingularity resolution
Planckian BHs astrophysical BHs
✔✔ ✔
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
Dymnikova ‘92, ‘96Hayward ‘06
...
Singularity-resolving spacetimes with deSitter core
Gambini, Pullin ‘08, ‘13
Modesto ‘10
Rovelli, Vidotto ‘14
Loop Quantum Gravity
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
Nicolini, Spallucci,Wondrak ‘19,...
Stringy Theory
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
Nicolini, Spallucci,Wondrak ‘19,...
Stringy Theory
Noncommutative spacetime structure
Nicolini, Smailagic,Spallucci ‘05
Generic result of (QG) singularity resolution?
Kerr (GR)
Kerr (regular / quantum)
– Thank you for your attention. –