Testing asymptotically safe quantum gravity through coupling to dynamical matter · 2014-09-02 ·...

Testing asymptotically safe quantum gravitythrough coupling to dynamical matter

Astrid Eichhorn

Perimeter Institute for Theoretical Physics

Experimental search for quantum gravity 2014, SISSA, Trieste

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 ofstandard model matter?

“Level 1” test:Can it accommodate new particles (dark matter, supersymmetry...)?

LHC, ADMX, ALPS... can test quantum gravity NOW

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 e i S →∫

spacetimes e−S

Goal:∫

spacetimes e−S

Goal:∫

spacetimes e− S

Asymptotic safety: quantum field theory of the metricgoal:

∫Dgµνe−S[gµν ]

−→∫p<k Dgµνe

−Γk [gµν ]

k → k + δk

Γk-‐δk

⇒ running couplings GN(k), λ(k)...

[S. Bethke, 2009]

−Γk [gµν ]

k → k + δk

Γk-‐δk

[S. Bethke, 2009]

−Γk [gµν ]

k → k + δk

Γk-‐δk

[S. Bethke, 2009]

Effective vs. fundamental QFTsQuantum Electrodynamics:

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

Effective theory

Quantum Chromodynamics:

asymptotic freedomno need for “new physics”

Fundamental theory

Effective theory

Fundamental theory

Effective theory

Fundamental theory

Asymptotic safety

βg = k∂kg(k)

gravity: [GN ] = −2

Asymptotic safety

interacting fixed point [Weinberg,

Asymptotic safety

βg = k∂kg(k)gravity: [GN ] = −2

Asymptotic safety

interacting fixed point [Weinberg,

Asymptotic safety

βg = k∂kg(k)gravity: [GN ] = −2

ææ G

Asymptotic safety

interacting fixed point[Weinberg, 1979]

Asymptotically Safe Quantum Gravity: EvidenceΓk EH = −1

16πGN(k)

∫ √g(R − 2λ(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

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

Compatibility with observations:Semiclassical gravity?

trajectory with GN → constand λ → const and measuredvalues in infrared

16πGN(k)

-0.1 0.0 0.1 0.2 0.3 0.4 0.5

16πGN(k)

-0.1 0.0 0.1 0.2 0.3 0.4 0.5

16πGN(k)

∫ √g(R − 2λ(k))

-0.1 0.0 0.1 0.2 0.3 0.4 0.5

Asymptotically Safe Quantum Gravity: Evidence

-0.1 0.0 0.1 0.2 0.3 0.4 0.5

Γk EH = −116πGN(k)

∫ √g(R − 2λ(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)

Asymptotically Safe Quantum Gravity: Evidence

-0.1 0.0 0.1 0.2 0.3 0.4 0.5

∫ √g(R − 2λ(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)

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 & matterfluctuations ⇒ gravity and matter matters!

Learning by example: Possible effects of matterQuantum Chromodynamics:

0.4 0.8 g

Nf < 16.5

Nf > 16.5

Asymptotic freedom only for Nf < 16.5

UV completion for gravity compatible with Standard Model?

Learning by example: Possible effects of matterQuantum Chromodynamics:

0.4 0.8 g

Nf < 16.5

Nf > 16.5

Asymptotic freedom only for Nf < 16.5

UV completion for gravity compatible with Standard Model?

Matter effects on the gravitational fixed pointwith P. Dona, R. Percacci (2013): Truncation of the effective action:

Γk = Γk EH + Γk matter

∫ √g(R − 2λ(k)) + Zh

∫ √ghµνMµνκλ

(−D2

)hκλ

ηh = −k∂k lnZh

βG , βλ

∫ √g(R − 2λ(k)) + Zh

(−D2

)hκλ

ηh = −k∂k lnZh

βG , βλ

∫ √g(R − 2λ(k)) + Zh

(−D2

)hκλ

ηh = −k∂k lnZh

βG , βλ

Γk = Γk EH + Γk matter with minimally coupled matter:

NS scalars: SS = ZS2

∫ddx√g gµν

∑Nsi=1 ∂µφ

i∂νφi

ηS = −k∂k lnZSηh

βG , βλ

∫ddx√g gµν

∑Nsi=1 ∂µφ

i∂νφi

ηS = −k∂k lnZS

βG , βλ

∫ddx√g gµν

∑Nsi=1 ∂µφ

i∂νφi

ηS = −k∂k lnZSηh

βG , βλ

ND Dirac fermions SD = iZD

∫ddx√g∑ND

i=1 ψi /∇ψi

ηD = −k∂k lnZD

βG , βλ

ND Dirac fermions SD = iZD

∫ddx√g∑ND

i=1 ψi /∇ψi

ηD = −k∂k lnZDηh

βG , βλ

NV Abelian vector bosons:SV = ZV

∫ddx√g∑NF

i=1 gµνgκλF i

µκFiνλ + ZV

∫ddx√g∑NF

(gµνDµA

ηV = −k∂k lnZV

βG , βλ

NV Abelian vector bosons:SV = ZV

∫ddx√g∑NF

i=1 gµνgκλF i

µκFiνλ + ZV

∫ddx√g∑NF

(gµνDµA

ηV = −k∂k lnZV

βG , βλ

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

Is the fixed point compatible with the standard model?

Perturbative analysis(neglect graviton and matter wave function renormalizations)

βG = 2G + G2

NS + 2ND − 4NV

− 46) ,

→ for a given number of vectors NV , there is an upper limit on thenumber of scalars NS and Dirac fermions ND !

Matter matters in asymptotically safe quantum gravity!

βG = 2G + G2

6π (NS + 2ND − 4NV − 46) ,

βG = 2G + G2

6π (NS + 2ND − 4NV − 46) ,

βG = 2G + G2

6π (NS + 2ND − 4NV − 46) ,

Fermions, scalars and the fixed point

æ æ æ æ æ æ æ æ æ ææ

5 10 15 20 25NS

æ æææææææ

5 10 15 20 25NS

æ æ æ æ ææ

à à à à àà

2 4 6 8ND

*, L�

scalars & fermions drive G∗ to divergence ⇒ upper limit on NS ,ND

Fermions, scalars and the fixed point

æ æ æ æ æ æ æ æ æ ææ

5 10 15 20 25NS

æ æææææææ

5 10 15 20 25NS

æ æ æ æ ææ

à à à à àà

2 4 6 8ND

*, L�

scalars & fermions drive G∗ to divergence ⇒ upper limit on NS ,ND

Vectors and the fixed point

æææææææææææææææææææææææææææææææææææææææææææææ

10 20 30 40 50NV

ææææææææææææææææææææææææææææææææææ

æææææææææ

10 20 30 40 50NV

vector degrees of freedom unrestricted by fixed-point requirement

Full analysis for NV = 12

10 20 30 40 50 60 70NS

upper limit on ND and NS

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

Specific matter models

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

→ right-handed neutrinos?X

→ dark matter scalar? X

→ axion? X

supersymmetric extension (MSSM: NS = 49,ND = 61/2,NV = 12) 7