The asymptotic-safety paradigm for quantum gravity

Transcription

1 The asymptotic-safety paradigm for quantum gravity Astrid Eichhorn Imperial College, London Helsinki workshop on quantum gravity June 1, 2016

2 Asymptotic safety Generalization of asymptotic freedom (! Standard Model of particle physics) provides quantum field theory for the metric: Dg µ e is[g µ ]

3 Motivation: Quantum field theory for metric

4 Motivation: Quantum field theory for metric Quantum Gravity hard to test experimentally

5 Motivation: Quantum field theory for metric Quantum Gravity hard to test experimentally Gravity at low energies tested experimentally Quantum theory at low energies tested experimentally

6 Motivation: Quantum field theory for metric Quantum Gravity hard to test experimentally Gravity at low energies tested experimentally Quantum theory at low energies tested experimentally ) assumptions for quantum gravity: metric carries quantum-gravity degrees of freedom

7 Motivation: Quantum field theory for metric Quantum Gravity hard to test experimentally Gravity at low energies tested experimentally Quantum theory at low energies tested experimentally ) assumptions for quantum gravity: metric carries quantum-gravity degrees of freedom framework: local continuum quantum field theory Dg µ e is[g µ ]

8 Motivation: Quantum field theory for metric Quantum Gravity hard to test experimentally Gravity at low energies tested experimentally Quantum theory at low energies tested experimentally ) assumptions for quantum gravity: metric carries quantum-gravity degrees of freedom framework: local continuum quantum field theory Dg µ e is[g µ ]! Dg µ e S[g µ ]

9 Quantum field theory for gravity Dg µ e is[g µ ]! Dg µ e S[g µ ]

10 Quantum field theory for gravity Dgµ e is[gµ ]! Dgµ e 1/k resolution scale S[gµ ]! p<k Dgµ e k [gµ ]

11 Quantum field theory for gravity Dg µ e is[g µ ]! Dg µ e S[g µ ]! p<k Dg µ e k[g µ ] 1/k resolution scale k k = 1 16 G N d 4 x p g(r 2 ) + effective action effective description microscopic description

12 Quantum field theory for gravity Dg µ e is[g µ ]! Dg µ e S[g µ ]! p<k Dg µ e k[g µ ] 1/k resolution scale k effective action k = 1 16 G N d 4 x p g(r 2 )+ V (r) =V Newton + V pn + Gm 1m 2 r Donoghue, G~ r

13 Quantum field theory for gravity Dg µ e is[g µ ]! Dg µ e S[g µ ]! p<k Dg µ e k[g µ ] 1/k resolution scale k effective action k = 1 16 G N d 4 x p g(r 2 )+ V (r) =V Newton + V pn + Gm 1m 2 r Donoghue, G~ r

14 Quantum field theory for gravity Dg µ e is[g µ ]! Dg µ e S[g µ ]! p<k Dg µ e k[g µ ] 1/k resolution scale k effective action k = 1 16 G N d 4 x p g(r 2 )+ What is the microscopic dynamics of gravity?

15 Quantum field theory for gravity Dg µ e is[g µ ]! Dg µ e S[g µ ]! p<k Dg µ e k[g µ ] 1/k resolution scale k effective action k = 1 16 G N d 4 x p g(r 2 )+ Asymptotic safety: Can we take k!1 to derive the microscopic dynamics of gravity?

16 Quantum field theory for gravity Dg µ e is[g µ ]! Dg µ e S[g µ ]! p<k Dg µ e k[g µ ] 1/k resolution scale k k = 1 16 G N (k) d 4 x p g(r 2 (k)) + + effective action What happens if k! k + k? running couplings in QFT (even if no UV-divergences) { 1/k e + (k)

17 Quantum field theory for gravity Dg µ e is[g µ ]! Dg µ e S[g µ ]! p<k Dg µ e k[g µ ] 1/k resolution scale k k = 1 16 G N (k) d 4 x p g(r 2 (k)) + effective action What happens if k! k + k? running couplings in QFT (even if no UV-divergences) What is the scale-dependence of the gravitational couplings?

18 Effective and fundamental QFTs QED e 2 HkL vacuum = screening medium Λ k

19 Effective and fundamental QFTs QED e 2 HkL vacuum = screening medium Λ k effective theory scale of new physics

20 Effective and fundamental QFTs QED QCD e 2 HkL vacuum = screening medium Λ k CMS collaboration, 2014 effective theory scale of new physics

21 Effective and fundamental QFTs QED QCD e 2 HkL vacuum = screening medium effective theory Λ k CMS collaboration, 2014 fundamental theory scale of new physics asymptotic freedom ) no need for new physics

22 Asymptotic freedom for gravity? g = k@ k g(k) asymptotic freedom non-interacting fixed point [Gross, Wilczek; Politzer] asymptotic freedom non-interacting fixed point [Gross, Wilczek; Politzer]

23 Asymptotic freedom for gravity? g = k@ k g(k) k = [G N ]= G N (k) d 4 x p 2 asymptotic freedom non-interacting fixed point [Gross, Wilczek; Politzer] asymptotic freedom non-interacting fixed point [Gross, Wilczek; Politzer]

24 Asymptotic freedom for gravity? g = k@ k g(k) k = [G N ]= G N (k) d 4 x p 2 asymptotic freedom non-interacting fixed point [Gross, Wilczek; Politzer] asymptotic freedom non-interacting fixed point [Gross, Wilczek; Politzer]

25 Asymptotic freedom for gravity? g = k@ k g(k) k = [G N ]= G N (k) d 4 x p 2 asymptotic freedom non-interacting fixed point [Gross, Wilczek; Politzer] asymptotic freedom non-interacting fixed point [Gross, Wilczek; Politzer] asymptotic safety interacting fixed point [Weinberg]

26 Asymptotic safety g3 Quantum fluctuations generate all interactions g1 g2

27 Asymptotic safety g3 Quantum fluctuations generate all interactions example: Quantum Electrodynamics g1 Euler Heisenberg = d 4 x 1 4 F 2 + c 1 (F 2 ) 2 + c 2 (F F ) 2 g2

28 Asymptotic safety g3 k = Quantum fluctuations generate all interactions d 4 x p 1 g 16 G N (k) (R 2 (k)) + X! i (k)r i +... i g1 microscopic dynamics g2

29 Asymptotic safety g3 UV-attractive direction = free parameter g1 g2

30 Asymptotic safety g3 UV-repulsive directions: predictions of asymptotic safety critical surface g1 g2

31 Asymptotic safety g3 UV-repulsive directions: predictions of asymptotic safety critical surface g1 g i (k) =g i + c i k k 0 i g2 i > 0 i < 0 relevant (free parameter) irrelevant (prediction)

32 Asymptotic safety g3 UV-repulsive directions: predictions of asymptotic safety critical surface g1 g2 asymptotic safety in a nutshell: interacting fixed point with finitely many relevant directions

33 Testing asymptotic safety: Functional Renormalization Group Wetterich equation: scale dependence of k k Wetterich 93 truncation: k = 1 16 G N (k) d 4 x p g (R 2 (k)) G(k) =G N k 2, (k) = (k)/k 2

34 Testing asymptotic safety: Functional Renormalization Group Wetterich equation: scale dependence of k k Wetterich truncation: k = 1 16 G N (k) d 4 x p g (R 2 (k)) G G(k) =G N k 2, (k) = (k)/k Wetterich equation: G, l Reuter, 96; Reuter, Saueressig 01, Litim, 03

35 Evidence for asymptotic safety in gravity k = G N (k) d 4 x p g (R 2 (k)) G(k) =G N k 2, (k) = (k)/k 2 interacting fixed point with 2 relevant directions 0.2 G l Reuter, 96; Reuter, Saueressig 01, Litim, 03

36 Evidence for asymptotic safety in gravity k = G N (k) d 4 x p g (R 2 (k)) G(k) =G N k 2, (k) = (k)/k 2 interacting fixed point with ~ 3 (?) relevant directions G l Reuter, 96; Reuter, Saueressig 01, Litim, 03 extended truncations: f(r) Reuter, Lauscher, 02; Codello, Percacci, Rahmede, 09; Benedetti, Caravelli, 12; Dietz, Morris, 12; Demmel, Saueressig, anusso, 15; A.E. 15 R 2, R µ R µ Benedetti, Machado, Saueressig, 09 C µ apple C apple C µ Gies, Knorr, Lippoldt, Saueressig, 16 Manrique, Reuter, Saueressig, 11; Christiansen, Litim, Pawlowski, Rodigast, 14; Codello, D Odorico, Pagani, 14; Becker, Reuter, 14, 15; Christiansen, Knorr, Meibohm, Pawlowski, Reichert, 15 Groh, Saueressig, 10; A.E., Gies, 10; A.E., 13

37 What happens at the Planck scale?

38 What happens at the Planck scale? Reuter, Saueressig, 01 G N (k) = G(k) k 2 Planck scale! G k 2 transition scale to fixed-point regime

39 What happens at the Planck scale? Reuter, Saueressig, 01 graviton-mediated photon scattering G N (k) = G(k) k 2 Planck scale ds@pd dw êfb ! G k 2 transition scale to fixed-point regime G N = const G N 1/p 2 G N (k) pêtev Doebrich, AE, 12

40 Towards the real world : adding matter

41 Towards the real world : adding matter Standard Model: u d e c s µ t b W ± g e µ H admits asymptotically safe gravitational fixed point (minimally coupled matter + Einstein-Hilbert) [Dona, A.E., Percacci 13, 14; Dona, A.E., Labus, Percacci 15] [Meibohm, Pawlowski, Reichert 15]

42 Higgs sector & quantum gravity

43 Higgs sector & quantum gravity V [H 2 ] yt g 3 k =... + m 2 hh 2 + H 4 + X y q H q R q L +.. q SM couplings g 2 g y b m in TeV l [Buttazzo et al. 13] RGE scale m in GeV y t (M Pl ) 0.4! M top 173 GeV y b (M Pl ) 0! M bottom 4GeV p

44 Higgs sector & quantum gravity yt g 3 assume: SM couplings g 2 g 1 no new physics below MPlanck! quantum gravity must allow y b m in TeV l [Buttazzo et al. 13] RGE scale m in GeV y t (M Pl ) 0.4! M top 173 GeV y b (M Pl ) 0! M bottom 4GeV p

45 Higgs sector & quantum gravity yt g 3 assume: SM couplings g 2 g 1 no new physics below MPlanck! quantum gravity must allow y b m in TeV l [Buttazzo et al. 13] RGE scale m in GeV y t (M Pl ) 0.4! M top 173 GeV y b (M Pl ) 0! M bottom 4GeV g p g2: UV- attractive (relevant): any value can be reached in IR g1: UV- repulsive (irrelevant): IR-value fixed g 1! Irrelevant couplings in the Higgs sector allow predictions

46 Yukawa coupling in quantum gravity

47 Yukawa coupling in quantum gravity toy model of the Higgs-Yukawa sector coupled to gravity: k = d 4 x p gg + i 2 d 4 x p g /r + iy d 4 x p g + k EH + S gf

48 Yukawa coupling in quantum gravity toy model of the Higgs-Yukawa sector coupled to gravity: k = d 4 x p gg + i 2 d 4 x p g /r + iy d 4 x p g + k EH + S gf y = y Gy+ y( /2+ ) qm fluc s of matter qm fluc s of gravity! fixed point at y =0 A.E., Held, Pawlowski 16

49 Yukawa coupling in quantum gravity toy model of the Higgs-Yukawa sector coupled to gravity: k = d 4 x p gg + i 2 d 4 x p g /r + iy d 4 x p g + k EH + S gf y = y Gy+ y( /2+ )! fixed point at y =0 A.E., Held, Pawlowski 16 G ! y 2! y(m Pl ) 0 UV-repulsive fixed point y

50 Yukawa coupling in quantum gravity toy model of the Higgs-Yukawa sector coupled to gravity: k = d 4 x p gg + i 2 d 4 x p g /r + iy d 4 x p g + k EH + S gf y = y Gy+ y( /2+ )! fixed point at y =0 A.E., Held, Pawlowski 16 G SM couplings yt g 3 g 2 g 1 y b m in TeV l [Buttazzo et al. 13]! y 2! y(m Pl ) 0 RGE scale m in GeV UV-repulsive fixed point y t (M Pl ) y! M top 173 GeV y b (M Pl ) 0! M bottom 4GeV

51 Yukawa coupling in quantum gravity toy model of the Higgs-Yukawa sector coupled to gravity: k = d 4 x p gg + i 2 d 4 x p g /r + iy d 4 x p g + k EH + S gf y = y Gy+ y( /2+ )! fixed point at y =0 A.E., Held, Pawlowski 16 G SM couplings yt g 3 g 2 g 1 y b m in TeV l [Buttazzo et al. 13]! y 2! y(m Pl ) 0 RGE scale m in GeV UV-repulsive fixed point y t (M Pl ) 0.4 outlook: - further matter fields of the Standard Model y! M top 173 GeV y b (M Pl ) 0! M bottom 4GeV! y t,y b

52 Summary: Asymptotic safety for gravity

53 Summary: Asymptotic safety for gravity main idea: interacting ultraviolet fixed point!qft for quantum gravity & matter

54 Summary: Asymptotic safety for gravity main idea: interacting ultraviolet fixed point!qft for quantum gravity & matter status: considerable evidence for fixed point in pure gravity with few relevant directions

55 Summary: Asymptotic safety for gravity main idea: interacting ultraviolet fixed point!qft for quantum gravity & matter status: considerable evidence for fixed point in pure gravity with few relevant directions towards quantum gravity in our universe: hints: standard model matter compatible with grav. fixed point

56 Summary: Asymptotic safety for gravity main idea: interacting ultraviolet fixed point!qft for quantum gravity & matter status: considerable evidence for fixed point in pure gravity with few relevant directions towards quantum gravity in our universe: hints: standard model matter compatible with grav. fixed point quantum gravity effects on matter: hints for irrelevance of Yukawa coupling! predictions at low energy!

57 Summary: Asymptotic safety for gravity main idea: interacting ultraviolet fixed point!qft for quantum gravity & matter status: considerable evidence for fixed point in pure gravity with few relevant directions towards quantum gravity in our universe: hints: standard model matter compatible with grav. fixed point quantum gravity effects on matter: hints for irrelevance of Yukawa coupling! predictions at low energy! exciting times lie ahead!