Testing asymptotically safe quantum gravity through coupling to - - PowerPoint PPT Presentation

▶
testing asymptotically safe quantum gravity through
SMART_READER_LITE
LIVE PREVIEW

Testing asymptotically safe quantum gravity through coupling to - - PowerPoint PPT Presentation

Mar 05, 2024 364 likes •1.08k views

Testing asymptotically safe quantum gravity through coupling to dynamical matter Astrid Eichhorn Perimeter Institute for Theoretical Physics Experimental search for quantum gravity 2014, SISSA, Trieste How to test quantum gravity

slide-1
SLIDE 1

Testing asymptotically safe quantum gravity through coupling to dynamical matter

Astrid Eichhorn

Perimeter Institute for Theoretical Physics

Experimental search for quantum gravity 2014, SISSA, Trieste

slide-2
SLIDE 2

How to test quantum gravity experimentally?

“direct” quantum gravity signals: challenging...

slide-3
SLIDE 3

How to test quantum gravity experimentally?

“direct” quantum gravity signals: challenging... (precision) data on particle physics available experimental quantum gravity tests: Compatibility with matter

slide-4
SLIDE 4

How to test quantum gravity experimentally?

“direct” quantum gravity signals: challenging... (precision) data on particle physics available experimental quantum gravity tests: Compatibility with matter “Level 0” test: Is a given model of quantum spacetime compatible with the existence of standard model matter?

slide-5
SLIDE 5

How to test quantum gravity experimentally?

“direct” quantum gravity signals: challenging... (precision) data on particle physics available experimental quantum gravity tests: Compatibility with matter “Level 0” test: Is a given model of quantum spacetime compatible with the existence of standard model matter? “Level 1” test: Can it accommodate new particles (dark matter, supersymmetry...)?

slide-6
SLIDE 6

How to test quantum gravity experimentally?

“direct” quantum gravity signals: challenging... (precision) data on particle physics available experimental quantum gravity tests: Compatibility with matter “Level 0” test: Is a given model of quantum spacetime compatible with the existence of standard model matter? “Level 1” test: Can it accommodate new particles (dark matter, supersymmetry...)? LHC, ADMX, ALPS... can test quantum gravity NOW

slide-7
SLIDE 7

Asymptotic safety: quantum field theory of the metric

slide-8
SLIDE 8

Asymptotic safety: quantum field theory of the metric

quantum fields: gravity:

slide-9
SLIDE 9

Asymptotic safety: quantum field theory of the metric

quantum fields: gravity: → quantum gravity: spacetime fluctuations

?

quantum theory of gravity in the path-integral framework: Goal:

  • spacetimes ei S

→

  • spacetimes e− S
slide-10
SLIDE 10

Asymptotic safety: quantum field theory of the metric

goal:

  • Dgµνe−S[gµν]
slide-11
SLIDE 11

Asymptotic safety: quantum field theory of the metric

goal:

  • Dgµνe−S[gµν]

− →

  • p<k Dgµνe−Γk[gµν]

k → k + δk g1 ¡ g2 ¡ g3 ¡ Γk ¡ Γk-­‑δk ¡ ⇒ running couplings GN(k), λ(k)...

slide-12
SLIDE 12

Asymptotic safety: quantum field theory of the metric

goal:

  • Dgµνe−S[gµν]

− →

  • p<k Dgµνe−Γk[gµν]

k → k + δk g1 ¡ g2 ¡ g3 ¡ Γk ¡ Γk-­‑δk ¡ ⇒ running couplings GN(k), λ(k)...

[S. Bethke, 2009]

slide-13
SLIDE 13

Effective vs. fundamental QFTs

Quantum Electrodynamics:

k e2HkL

Λ

slide-14
SLIDE 14

Effective vs. fundamental QFTs

Quantum Electrodynamics:

k e2HkL

Λ

running coupling diverges ⇒ Λ is scale of “new physics” Effective theory

slide-15
SLIDE 15

Effective vs. fundamental QFTs

Quantum Electrodynamics:

k e2HkL

Λ

running coupling diverges ⇒ Λ is scale of “new physics” Effective theory Quantum Chromodynamics:

k Αk

asymptotic freedom no need for “new physics” Fundamental theory

slide-16
SLIDE 16

Asymptotic safety

βg = k∂kg(k)

slide-17
SLIDE 17

Asymptotic safety

βg = k∂kg(k) gravity: [GN] = −2

G ΒG

slide-18
SLIDE 18

Asymptotic safety

βg = k∂kg(k) gravity: [GN] = −2

  • G

ΒG

Asymptotic safety interacting fixed point

[Weinberg, 1979]

slide-19
SLIDE 19

Asymptotically Safe Quantum Gravity: Evidence

Γk EH =

−1 16πGN(k)

√g(R − 2¯ λ(k)) (Wetterich-equation) G = GNk2 and λ = ¯ λ/k2 fixed point in dimensionless couplings → scale-free regime

slide-20
SLIDE 20

Asymptotically Safe Quantum Gravity: Evidence

Γk EH =

−1 16πGN(k)

√g(R − 2¯ λ(k)) (Wetterich-equation) G = GNk2 and λ = ¯ λ/k2 fixed point in dimensionless couplings → scale-free regime

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 Λ G

[M. Reuter, 1996; M. Reuter, F.Saueressig, 2001; D. Litim, 2004]

slide-21
SLIDE 21

Asymptotically Safe Quantum Gravity: Evidence

Γk EH =

−1 16πGN(k)

√g(R − 2¯ λ(k)) (Wetterich-equation) G = GNk2 and λ = ¯ λ/k2 fixed point in dimensionless couplings → scale-free regime

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 Λ G

[M. Reuter, 1996; M. Reuter, F.Saueressig, 2001; D. Litim, 2004]

Compatibility with observations: Semiclassical gravity?

slide-22
SLIDE 22

Asymptotically Safe Quantum Gravity: Evidence

Γk EH =

−1 16πGN(k)

√g(R − 2¯ λ(k)) G = GNk2 and λ = ¯ λ/k2 fixed point in dimensionless couplings → scale-free regime

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 Λ G

[M. Reuter, 1996; M. Reuter, F.Saueressig, 2001; D. Litim, 2004]

Compatibility with observations: Semiclassical gravity? trajectory with GN → const and ¯ λ → const and measured values in infrared

slide-23
SLIDE 23

Asymptotically Safe Quantum Gravity: Evidence

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 Λ G

Γk EH =

−1 16πGN(k)

√g(R − 2¯ λ(k)) fixed-point action: prediction

slide-24
SLIDE 24

Asymptotically Safe Quantum Gravity: Evidence

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 Λ G

Γk EH =

−1 16πGN(k)

√g(R − 2¯ λ(k)) fixed-point action: prediction Γk = Γk EH + Γgauge−fixing + Γghost + √g (f (R) + RµνRµν + ....)

  • E. Manrique, M. Reuter, F. Saueressig (2009, 2010);
  • I. Donkin, J. Pawlowski (2012);
  • A. Codello, G. D’Odorico, C. Pagani (2013)

A.E., H.Gies, M.Scherer (2009), A.E., H. Gies (2010), A.E. (2013)

  • A. Codello, R. Percacci, C. Rahmede (2008);

D.Benedetti, F. Caravelli (2012);

  • K. Falls, D. Litim, K. Nikolakopoulos (2013);
  • J. Dietz, T. Morris (2013);
  • M. Demmel, F. Saueressig, O. Zanusso (2014)
  • D. Benedetti, P. Machado, F. Saueressig (2009)
slide-25
SLIDE 25

What matters in quantum gravity

Universe contains gravity & matter

slide-26
SLIDE 26

What matters in quantum gravity

Universe contains gravity & matter interaction between these cannot be switched off

  • ddx√ggµν∂µφ∂νφ

− → ...

slide-27
SLIDE 27

What matters in quantum gravity

Universe contains gravity & matter interaction between these cannot be switched off

  • ddx√ggµν∂µφ∂νφ

− → ... RG flow in gravity and matter sector driven by metric & matter fluctuations ⇒ gravity and matter matters!

slide-28
SLIDE 28

Learning by example: Possible effects of matter

Quantum Chromodynamics:

0.4 0.8 g

  • 0.01

0.01 bg QCD

Nf < 16.5 Nf > 16.5

Asymptotic freedom only for Nf < 16.5

slide-29
SLIDE 29

Learning by example: Possible effects of matter

Quantum Chromodynamics:

0.4 0.8 g

  • 0.01

0.01 bg QCD

Nf < 16.5 Nf > 16.5

Asymptotic freedom only for Nf < 16.5 UV completion for gravity compatible with Standard Model?

slide-30
SLIDE 30

Matter effects on the gravitational fixed point

with P. Don´ a, R. Percacci (2013): Truncation of the effective action: Γk = Γk EH + Γk matter Γk EH =

−1 16πGN(k)

√g(R − 2¯ λ(k)) + Zh

2

√ghµνMµνκλ

  • −D2

hκλ

slide-31
SLIDE 31

Matter effects on the gravitational fixed point

with P. Don´ a, R. Percacci (2013): Truncation of the effective action: Γk = Γk EH + Γk matter Γk EH =

−1 16πGN(k)

√g(R − 2¯ λ(k)) + Zh

2

√ghµνMµνκλ

  • −D2

hκλ ηh = −k∂k ln Zh

slide-32
SLIDE 32

Matter effects on the gravitational fixed point

with P. Don´ a, R. Percacci (2013): Truncation of the effective action: Γk = Γk EH + Γk matter Γk EH =

−1 16πGN(k)

√g(R − 2¯ λ(k)) + Zh

2

√ghµνMµνκλ

  • −D2

hκλ ηh = −k∂k ln Zh βG, βλ

slide-33
SLIDE 33

Matter effects on the gravitational fixed point

with P. Don´ a, R. Percacci (2013): Truncation of the effective action: Γk = Γk EH + Γk matter with minimally coupled matter:

slide-34
SLIDE 34

Matter effects on the gravitational fixed point

with P. Don´ a, R. Percacci (2013): Truncation of the effective action: Γk = Γk EH + Γk matter with minimally coupled matter: NS scalars: SS = ZS

2

  • ddx√g gµν Ns

i=1 ∂µφi∂νφi

ηS = −k∂k ln ZS

slide-35
SLIDE 35

Matter effects on the gravitational fixed point

with P. Don´ a, R. Percacci (2013): Truncation of the effective action: Γk = Γk EH + Γk matter with minimally coupled matter: NS scalars: SS = ZS

2

  • ddx√g gµν Ns

i=1 ∂µφi∂νφi

ηS = −k∂k ln ZS ηh βG, βλ

slide-36
SLIDE 36

Matter effects on the gravitational fixed point

with P. Don´ a, R. Percacci (2013): Truncation of the effective action: Γk = Γk EH + Γk matter with minimally coupled matter: ND Dirac fermions SD = iZD

  • ddx√g ND

i=1 ¯

ψi / ∇ψi ηD = −k∂k ln ZD

slide-37
SLIDE 37

Matter effects on the gravitational fixed point

with P. Don´ a, R. Percacci (2013): Truncation of the effective action: Γk = Γk EH + Γk matter with minimally coupled matter: ND Dirac fermions SD = iZD

  • ddx√g ND

i=1 ¯

ψi / ∇ψi ηD = −k∂k ln ZD ηh βG, βλ

slide-38
SLIDE 38

Matter effects on the gravitational fixed point

with P. Don´ a, R. Percacci (2013): Truncation of the effective action: Γk = Γk EH + Γk matter with minimally coupled matter: NV Abelian vector bosons: SV = ZV

4

  • ddx√g NF

i=1 gµνgκλF i µκF i νλ + ZV 2ξ

  • ddx√¯

g NF

i=1

  • ¯

gµν ¯ DµAi

ν

2 ηV = −k∂k ln ZV

slide-39
SLIDE 39

Matter effects on the gravitational fixed point

with P. Don´ a, R. Percacci (2013): Truncation of the effective action: Γk = Γk EH + Γk matter with minimally coupled matter: NV Abelian vector bosons: SV = ZV

4

  • ddx√g NF

i=1 gµνgκλF i µκF i νλ + ZV 2ξ

  • ddx√¯

g NF

i=1

  • ¯

gµν ¯ DµAi

ν

2 ηV = −k∂k ln ZV ηh βG, βλ

slide-40
SLIDE 40

Matter effects on the gravitational fixed point

→ βG, βλ, ηh ηc, ηS, ηD, ηV

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 Λ G

???

Is the fixed point compatible with the standard model?

slide-41
SLIDE 41

Perturbative analysis

(neglect graviton and matter wave function renormalizations) βG = 2G + G 2

6π (

− 46) ,

slide-42
SLIDE 42

Perturbative analysis

(neglect graviton and matter wave function renormalizations) βG = 2G + G 2

6π (NS + 2ND − 4NV − 46) ,

slide-43
SLIDE 43

Perturbative analysis

(neglect graviton and matter wave function renormalizations) βG = 2G + G 2

6π (NS + 2ND − 4NV − 46) ,

slide-44
SLIDE 44

Perturbative analysis

(neglect graviton and matter wave function renormalizations) βG = 2G + G 2

6π (NS + 2ND − 4NV − 46) ,

→ for a given number of vectors NV , there is an upper limit on the number of scalars NS and Dirac fermions ND! Matter matters in asymptotically safe quantum gravity!

slide-45
SLIDE 45

Fermions, scalars and the fixed point

  • 5

10 15 20 25 NS 1 2 5 10 20 50 100 200 G

  • 5

10 15 20 25 NS 0.05 0.10 0.15 0.20 0.25 0.30

slide-46
SLIDE 46

Fermions, scalars and the fixed point

  • 5

10 15 20 25 NS 1 2 5 10 20 50 100 200 G

  • 5

10 15 20 25 NS 0.05 0.10 0.15 0.20 0.25 0.30

  • 2

4 6 8 ND 10 5 5 10 G

  • ,
  • scalars & fermions drive G∗ to divergence ⇒ upper limit on NS, ND
slide-47
SLIDE 47

Vectors and the fixed point

  • 10

20 30 40 50 NV 0.1 0.2 0.3 0.4 0.5 0.6 0.7 G

  • 10

20 30 40 50 NV 0.05 0.10 0.15 0.20 0.25 0.30

  • vector degrees of freedom unrestricted by fixed-point requirement
slide-48
SLIDE 48

Full analysis for NV = 12

10 20 30 40 50 60 70 NS 10 20 30 40 ND

upper limit on ND and NS Standard Model: NV = 12, ND = 45/2, NS = 4: compatible with gravitational fixed point

slide-49
SLIDE 49

Specific matter models

Standard Model: (NS = 4, ND = 45/2, NV = 12)

slide-50
SLIDE 50

Specific matter models

Standard Model: (NS = 4, ND = 45/2, NV = 12) → right-handed neutrinos? → dark matter scalar? → axion?

slide-51
SLIDE 51

Specific matter models

Standard Model: (NS = 4, ND = 45/2, NV = 12) → right-handed neutrinos? → dark matter scalar? → axion? supersymmetric extension (MSSM: NS = 49, ND = 61/2, NV = 12) ✗

slide-52
SLIDE 52

Specific matter models

Standard Model: (NS = 4, ND = 45/2, NV = 12) → right-handed neutrinos? → dark matter scalar? → axion? supersymmetric extension (MSSM: NS = 49, ND = 61/2, NV = 12) ✗ GUT (SO(10): NS = 97, ND = 24, NV = 45) ✗

slide-53
SLIDE 53

Specific matter models

Standard Model: (NS = 4, ND = 45/2, NV = 12) → right-handed neutrinos? → dark matter scalar? → axion? supersymmetric extension (MSSM: NS = 49, ND = 61/2, NV = 12) ✗ GUT (SO(10): NS = 97, ND = 24, NV = 45) ✗ Only specific models with restricted matter content are compatible with Asymptotically Safe Quantum Gravity within our truncation

slide-54
SLIDE 54

Tests of quantum gravity

Does testing quantum gravity require galaxy-size accelerators? Possibly could test Asymptotically Safe Quantum Gravity at LHC, 14 TeV: Look for Beyond-Standard-Model particle physics experimental searches for weakly-coupled low-mass particles (dark matter) might also test quantum gravity

slide-55
SLIDE 55

Extra dimensions

[J. Pivarski]

slide-56
SLIDE 56

Extra dimensions

[J. Pivarski]

Extra dimensions in asymptotic safety? pure-gravity fixed point exists in d ≥ 4 (Einstein-Hilbert

[Fischer, Litim, 2006] and higher

derivatives [Ohta, Percacci, 2013])

slide-57
SLIDE 57

Extra dimensions

[J. Pivarski]

Extra dimensions in asymptotic safety? pure-gravity fixed point exists in d ≥ 4 (Einstein-Hilbert

[Fischer, Litim, 2006] and higher

derivatives [Ohta, Percacci, 2013])

10 20 30 40 50 60 NS 5 10 15 20 25 N D

10 20 30 40 50 60 NS 2 4 6 8 10 ND

5d 6d → universal extra dimensions restricted [P.Don`

a, A.E., R. Percacci, 2013]

slide-58
SLIDE 58

The Higgs – new compatibility tests for quantum gravity?

slide-59
SLIDE 59

The Higgs – new compatibility tests for quantum gravity?

Higgs mass mH ∼ √λ4

L l4

λ4

slide-60
SLIDE 60

The Higgs – new compatibility tests for quantum gravity?

Higgs mass mH ∼ √λ4

L l4

λ4

  • 107

109 1011 1013 1015 1017 1019 140. 145. 150. 155. 160. GeV mHGeV

Higgs mass bound in toy model

slide-61
SLIDE 61

The Higgs – new compatibility tests for quantum gravity?

Higgs mass mH ∼ √λ4

L l4

λ4

  • 107

109 1011 1013 1015 1017 1019 140. 145. 150. 155. 160. GeV mHGeV

Higgs mass bound in toy model

Where is Planck-scale physics/ quantum gravity? underlying assumption: Vφ(Λ) = m2φ2 + λ4φ4 + λ6φ6 + ... with λ6(Λ) = λ8(Λ) = 0

slide-62
SLIDE 62

The Higgs – new compatibility tests for quantum gravity?

Higgs mass mH ∼ √λ4

L l4

λ4

  • 107

109 1011 1013 1015 1017 1019 140. 145. 150. 155. 160. GeV mHGeV

Higgs mass bound in toy model

Where is Planck-scale physics/ quantum gravity? underlying assumption: Vφ(Λ) = m2φ2 + λ4φ4 + λ6φ6 + ... with λ6(Λ) = λ8(Λ) = 0 quantum gravity:

slide-63
SLIDE 63

Higgs mass and Planck-scale physics

expect from Planck-scale physics (quantum gravity): λ6(Λ) = 0, λ8(Λ) = 0 example: λi(Λ) = 0, λ4(Λ) = 0, λ6(Λ) = 3, λ4(Λ) = −0.1, λ6(Λ) = 2

  • 107

109 1011 1013 1015 1017 1019 125. 130. 135. 140. 145. 150. 155. 160. GeV mHGeV

[A.E., M. Scherer, 2014 & A.E., J. J¨ ackel, T. Plehn and M. Scherer, in progress]

slide-64
SLIDE 64

Higgs mass and Planck-scale physics

expect from Planck-scale physics (quantum gravity): λ6(Λ) = 0, λ8(Λ) = 0 example: λi(Λ) = 0, λ4(Λ) = 0, λ6(Λ) = 3, λ4(Λ) = −0.1, λ6(Λ) = 2

  • 107

109 1011 1013 1015 1017 1019 125. 130. 135. 140. 145. 150. 155. 160. GeV mHGeV

[A.E., M. Scherer, 2014 & A.E., J. J¨ ackel, T. Plehn and M. Scherer, in progress]

Higgs mass sensitive to UV physics! Outlook: predict Higgs mass from quantum gravity, compare to measured value mH ≈ 125 GeV

slide-65
SLIDE 65

Summary & Outlook

Matter matters in (asymptotically safe) quantum gravity Asymptotic safety only viable for standard model and “small” extensions within truncated RG flow (unless assume very large number of vectors) Experimental tests of quantum gravity possible (search for Beyond-Standard-Model physics at LHC and low-mass particle search experiments) Outlook: Higgs mass sensitive to UV physics: New test for quantum gravity!

slide-66
SLIDE 66

Summary & Outlook

Matter matters in (asymptotically safe) quantum gravity Asymptotic safety only viable for standard model and “small” extensions within truncated RG flow (unless assume very large number of vectors) Experimental tests of quantum gravity possible (search for Beyond-Standard-Model physics at LHC and low-mass particle search experiments) Outlook: Higgs mass sensitive to UV physics: New test for quantum gravity!

Thank you for your attention!

slide-67
SLIDE 67

Setting a scale in quantum gravity

RG: sort quantum fluctuations according to momentum flat background: p2 curved background: D2 fluctuating spacetime?

slide-68
SLIDE 68

Setting a scale in quantum gravity

RG: sort quantum fluctuations according to momentum flat background: p2 curved background: D2 fluctuating spacetime? background field method: gµν = ¯ gµν + hµν

  • Dgµνe−S[gµν] =
  • Dhµνe−S[¯

gµν+hµν]

¯ D2 → short/long wavelength quantum fluctuations → hµν Rk(¯ D2) hµν

slide-69
SLIDE 69

Setting a scale in quantum gravity

RG: sort quantum fluctuations according to momentum flat background: p2 curved background: D2 fluctuating spacetime? background field method: gµν = ¯ gµν + hµν

  • Dgµνe−S[gµν] =
  • Dhµνe−S[¯

gµν+hµν]

¯ D2 → short/long wavelength quantum fluctuations → hµν Rk(¯ D2) hµν action symmetric under ¯ gµν → ¯ gµν + ǫγµν, hµν → hµν − ǫγµν broken by regulator! ⇒ background couplings = fluctuation couplings