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 experimentally? “direct” quantum gravity signals: challenging...
How to test quantum gravity experimentally? “direct” quantum gravity signals: challenging... (precision) data on particle physics available experimental quantum gravity tests: Compatibility with matter
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?
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...)?
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
Asymptotic safety: quantum field theory of the metric
Asymptotic safety: quantum field theory of the metric gravity: quantum fields:
Asymptotic safety: quantum field theory of the metric gravity: quantum fields: → quantum gravity: ? spacetime fluctuations quantum theory of gravity in the path-integral framework: � spacetimes e i S � spacetimes e − S Goal: →
Asymptotic safety: quantum field theory of the metric D g µν e − S [ g µν ] � goal:
Asymptotic safety: quantum field theory of the metric g 1 ¡ D g µν e − S [ g µν ] � goal: Γ k-‑δk ¡ p < k D g µν e − Γ k [ g µν ] � − → Γ k ¡ k → k + δ k g 2 ¡ g 3 ¡ ⇒ running couplings G N ( k ) , λ ( k ) ...
Asymptotic safety: quantum field theory of the metric g 1 ¡ D g µν e − S [ g µν ] � goal: Γ k-‑δk ¡ p < k D g µν e − Γ k [ g µν ] � − → Γ k ¡ k → k + δ k g 2 ¡ g 3 ¡ ⇒ running couplings G N ( k ) , λ ( k ) ... [S. Bethke, 2009]
Effective vs. fundamental QFTs Quantum Electrodynamics: e 2 H k L k Λ
Effective vs. fundamental QFTs Quantum Electrodynamics: e 2 H k L k Λ running coupling diverges ⇒ Λ is scale of “new physics” Effective theory
Effective vs. fundamental QFTs Quantum Chromodynamics: Quantum Electrodynamics: Α � k � e 2 H k L k Λ k running coupling diverges ⇒ Λ is scale of “new physics” asymptotic freedom no need for “new physics” Effective theory Fundamental theory
Asymptotic safety β g = k ∂ k g ( k )
Asymptotic safety gravity: [ G N ] = − 2 β g = k ∂ k g ( k ) Β G G
Asymptotic safety gravity: [ G N ] = − 2 β g = k ∂ k g ( k ) Β G G � Asymptotic safety interacting fixed point [Weinberg, 1979]
Asymptotically Safe Quantum Gravity: Evidence � √ g ( R − 2¯ − 1 Γ k EH = λ ( k )) (Wetterich-equation) 16 π G N ( k ) G = G N k 2 and λ = ¯ λ/ k 2 fixed point in dimensionless couplings → scale-free regime
Asymptotically Safe Quantum Gravity: Evidence � √ g ( R − 2¯ − 1 Γ k EH = λ ( k )) (Wetterich-equation) 16 π G N ( k ) G = G N k 2 and λ = ¯ λ/ k 2 fixed point in dimensionless couplings → scale-free regime 0.4 0.3 0.2 G 0.1 0.0 � 0.1 � 0.1 0.0 0.1 0.2 0.3 0.4 0.5 Λ [M. Reuter, 1996; M. Reuter, F.Saueressig, 2001; D. Litim, 2004]
Asymptotically Safe Quantum Gravity: Evidence � √ g ( R − 2¯ − 1 Γ k EH = λ ( k )) (Wetterich-equation) 16 π G N ( k ) G = G N k 2 and λ = ¯ λ/ k 2 fixed point in dimensionless couplings → scale-free regime 0.4 0.3 0.2 Compatibility with observations: G Semiclassical gravity? 0.1 0.0 � 0.1 � 0.1 0.0 0.1 0.2 0.3 0.4 0.5 Λ [M. Reuter, 1996; M. Reuter, F.Saueressig, 2001; D. Litim, 2004]
Asymptotically Safe Quantum Gravity: Evidence � √ g ( R − 2¯ − 1 Γ k EH = λ ( k )) 16 π G N ( k ) G = G N k 2 and λ = ¯ λ/ k 2 fixed point in dimensionless couplings → scale-free regime 0.4 0.3 0.2 Compatibility with observations: G Semiclassical gravity? 0.1 0.0 trajectory with G N → const and ¯ λ → const and measured � 0.1 values in infrared � 0.1 0.0 0.1 0.2 0.3 0.4 0.5 Λ [M. Reuter, 1996; M. Reuter, F.Saueressig, 2001; D. Litim, 2004]
Asymptotically Safe Quantum Gravity: Evidence 0.4 0.3 � √ g ( R − 2¯ 0.2 − 1 Γ k EH = λ ( k )) 16 π G N ( k ) G 0.1 fixed-point action: prediction 0.0 � 0.1 � 0.1 0.0 0.1 0.2 0.3 0.4 0.5 Λ
Asymptotically Safe Quantum Gravity: Evidence 0.4 0.3 � √ g ( R − 2¯ 0.2 − 1 Γ k EH = λ ( k )) 16 π G N ( k ) G 0.1 fixed-point action: prediction 0.0 � 0.1 � 0.1 0.0 0.1 0.2 0.3 0.4 0.5 � √ g ( f ( R ) + R µν R µν + .... ) Λ Γ k = Γ k EH + Γ gauge − fixing + Γ ghost + A. Codello, R. Percacci, C. Rahmede (2008); E. Manrique, M. Reuter, F. Saueressig (2009, 2010); D.Benedetti, F. Caravelli (2012); I. Donkin, J. Pawlowski (2012); K. Falls, D. Litim, K. Nikolakopoulos (2013); A. Codello, G. D’Odorico, C. Pagani (2013) J. Dietz, T. Morris (2013); A.E., H.Gies, M.Scherer (2009), A.E., H. Gies (2010), M. Demmel, F. Saueressig, O. Zanusso (2014) A.E. (2013) D. Benedetti, P. Machado, F. Saueressig (2009)
What matters in quantum gravity Universe contains gravity & matter
What matters in quantum gravity Universe contains gravity & matter interaction between these cannot be switched off d d x √ gg µν ∂ µ φ∂ ν φ ... � − →
What matters in quantum gravity Universe contains gravity & matter interaction between these cannot be switched off d d x √ gg µν ∂ µ φ∂ ν φ ... � − → RG flow in gravity and matter sector driven by metric & matter fluctuations ⇒ gravity and matter matters!
Learning by example: Possible effects of matter Quantum Chromodynamics: b g QCD N f > 16.5 0.01 g 0.4 0.8 - 0.01 N f < 16.5 Asymptotic freedom only for N f < 16 . 5
Learning by example: Possible effects of matter Quantum Chromodynamics: b g QCD N f > 16.5 0.01 g 0.4 0.8 - 0.01 N f < 16.5 Asymptotic freedom only for N f < 16 . 5 UV completion for gravity compatible with Standard Model?
Matter effects on the gravitational fixed point with P. Don´ a, R. Percacci (2013): Truncation of the effective action: Γ k = Γ k EH + Γ k matter � √ g ( R − 2¯ � √ gh µν M µνκλ − 1 λ ( k )) + Z h − D 2 � � Γ k EH = h κλ 16 π G N ( k ) 2
Matter effects on the gravitational fixed point with P. Don´ a, R. Percacci (2013): Truncation of the effective action: Γ k = Γ k EH + Γ k matter � √ g ( R − 2¯ � √ gh µν M µνκλ − 1 λ ( k )) + Z h − D 2 � � Γ k EH = h κλ 16 π G N ( k ) 2 η h = − k ∂ k ln Z h
Matter effects on the gravitational fixed point with P. Don´ a, R. Percacci (2013): Truncation of the effective action: Γ k = Γ k EH + Γ k matter � √ g ( R − 2¯ � √ gh µν M µνκλ − 1 λ ( k )) + Z h − D 2 � � Γ k EH = h κλ 16 π G N ( k ) 2 β G , β λ η h = − k ∂ k ln Z h
Matter effects on the gravitational fixed point with P. Don´ a, R. Percacci (2013): Truncation of the effective action: Γ k = Γ k EH + Γ k matter with minimally coupled matter:
Matter effects on the gravitational fixed point with P. Don´ a, R. Percacci (2013): Truncation of the effective action: Γ k = Γ k EH + Γ k matter with minimally coupled matter: d d x √ g g µν � N s N S scalars: S S = Z S i =1 ∂ µ φ i ∂ ν φ i � 2 η S = − k ∂ k ln Z S
Matter effects on the gravitational fixed point with P. Don´ a, R. Percacci (2013): Truncation of the effective action: Γ k = Γ k EH + Γ k matter with minimally coupled matter: d d x √ g g µν � N s N S scalars: S S = Z S i =1 ∂ µ φ i ∂ ν φ i � 2 β G , β λ η S = − k ∂ k ln Z S η h
Matter effects on the gravitational fixed point with P. Don´ a, R. Percacci (2013): Truncation of the effective action: Γ k = Γ k EH + Γ k matter with minimally coupled matter: d d x √ g � N D ψ i / i =1 ¯ ∇ ψ i � N D Dirac fermions S D = iZ D η D = − k ∂ k ln Z D
Matter effects on the gravitational fixed point with P. Don´ a, R. Percacci (2013): Truncation of the effective action: Γ k = Γ k EH + Γ k matter with minimally coupled matter: d d x √ g � N D ψ i / i =1 ¯ ∇ ψ i � N D Dirac fermions S D = iZ D β G , β λ η D = − k ∂ k ln Z D η h
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