A Holographic S tudy of Thermalization in Strongly C oupled P lasmas

1. Masaki Shigemori(KMI Nagoya) A Holographic Study of Thermalization inStrongly Coupled Plasmas KEK, 21 June 2011

2. Collaborators (Arxiv: 1012.4753, 1103.2683) Vijay Balasubramanian (U Penn),Berndt Müller (Duke) Alice Bernamonti, Ben Craps, Neil Copland, Wieland Staessens (VU Brussels) Jan de Boer (Amsterdam) Esko Keski-Vakkuri (Helsinki) Andreas Schäfer (Regensburg)

3. An old & new question What happens in nuclear matterat high temperature? Low T High T ~1012 Kelvin quarks, gluons: confined quarks, gluons: deconfined Quark-Gluon Plasma (QGP)

4. Heavy ion collision • QGP created at RHIC, LHC • “Little Bang” • Strongly coupled • Difficult to study heavy nucleus heavy nucleus QGP • Perturbative QCD: not applicable • Lattice simulations: not always powerful enough

5. Holographic approach • Equilibrated QGP • HI collision • Thermalization • AdS black hole • Energy injection? • BH formation AdS/CFT = “~” QCD SYM AdS string • A toy model for QCD • General insights into strongly coupled physics

6. Questions we ask & (try to) answer • What is the measure for thermalization in the bulk? • Local operators are not sufficient, etc. • Non-local operators do better job, etc. • What is the thermalization time? When observables become identical to the thermal ones AdS boundary local op nonlocal op

7. Outline 0. Intro 1. Review 1.1 HI collision 1.2 Lattice 1.3 Holographic approach 2. Holographic thermalization 2.1 Models & probes for therm’n 2.2 The model & results 2.3 Summary Mostly based on Casalderrey-Solana et al. 1101.0618

8. 1.1 QCD and heavy ion collision

9. QCD at high T • Conjectured phase diagram Taken from FAIR website

10. Heavy Ion Collision Idea: collision non-equilibriumstate equilibratedQGP freeze-out Actual: Taken from BNL website

11. Scales in HI collision (1) fm = Fermi = femtometer = m sec = 3 yoctoseconds Aunucleus p n hydrogen atom:

12. Scales in HI collision (2) RHIC: Au LHC: Pb Energy density on collision (RHIC, 5x crossover energy density) 8000 hadrons produced(RHIC)

13. Stages in HI collision chemicalfreezeout (hadronization) thermalization time kinematic freezeout collision hydrodynamic evolution equilibration non-equilibrium state equilibrated QGP hadronic gas (cf. ) energy density ~10 GeV/fm3 (RHIC, t=0.4 fm) ~60 GeV/fm3 (LHC, t=0.25 fm)

14. Bjorken flow • Boost invariance (in central rapidity region) phenomenologically confirmed (beam direction)

15. Elliptic flow more hadrons “elliptic flow” parametrizes asymmetryin hadron multiplicity beam direction is important for determining hydro properties of QGP less

16. Phenomenology of HI collision (1) • Ideal hydro after explains • Very fast thermalization • Larger spoils agreement • Perturbative QCD fails:

17. Phenomenology of HI collision (2) • QGP has very small shear viscosity - entropy density ratio: • The smallest observed in nature (water ~380, helium ~9)(ultracold atoms at the unitarity point has similar ) • Perturbative QCD fails: • Short mean-free-path no well-defined quasiparticle • Strongly coupled; perturbative approach invalid • LHC: comparably strongly coupled; comparably small

18. Phenomenology of HI collision (3) • All hadron species emerge from a single common fluid • Baryon chemical potential is small: • Jet quenching: You are here! jet • Medium modifies jets • Jets modifies medium quark plowing through QGP

19. Phenomenology of HI collision (4) • Quarkonia: mesons made of proton =  production suppressed

20. A field theory model of HI collision • Color glass condensate collision multiplicity mesons color flux nucleons with large rapidity rapidity Most particles originate from the “wake” of the nuclei

21. 1.2 Lattice approach

22. Lattice QCD (1) • Good at thermodynamics • Deconfinement is crossover • More conformal for larger (but non-conformal at ) • Still, deconfined (Polyakov loop ≠ 0) • Made of quarks & gluons • But can’t be treated perturbatively sites in one dir trace anomaly CFT is not a crazy model

23. Lattice QCD (2) • At pioneering stage about transport properties • Real-time correlators difficult • Shear viscosity • Not (yet) applicable to non-equilibrium properties

24. 1.3 Holographic approach

25. Holographic approach • Want to study strongly coupled phenomena in QCD • Toy model: SYM holo. dual String theoryin AdS5 SYM AdS/CFT Strong coupling Vacuum Thermal state(equilibrated plasma) Thermalization Weak coupling Empty AdS5 AdS BH BH formation horizon AdS boundary IR UV

26. Difference between QCD and • Is SYM really “similar” to QCD??? • QCD confines at low T, but doesn’t confineAt QCD deconfines and is similar to • is CFT but QCD isn’t QCD is near conformal at high T ( achieved initially) • is supersymmetric but QCD isn’t at T>0, susy broken • QCD is asymptotically free Experiments suggest it’s strongly coupled at high T …

27. Holo approach: equilibrium • Shear viscosity Holography: [Policastro+Son+Starinets]… Cf. weak coupling: theory (A,B) dependent universal • No quasiparticles • No propagating light DoFsOnly quasi-normal modes (same as QGP)

28. Holoapproach: near-equilibrium • Parton energy loss[Herzog et al.][Gubser] • Brownian motion / transverse momentum broadening Brownian motion force • Quark = string ending on boundary • Extract drag coeff / diffusion const. [de Boer+Hubeny+Rangamani+MS][Son+Teaney]… • Can derive Langevin eq.

29. 2. Probing thermalizationby holography

30. Non-equilibrium phenomena • (Near-)equilibrium physics (dual: BH) • Well-studied as we saw • Thermalization process (dual: BH formation) • Poorly understood • Occurs fast: (cf. ) • pQCD not applicable • Lattice QCD insufficient • Non-equil. physics of strongly coupled systems:terra incognita

31. Basics of holography • AdS spacetime AdSboundary AdS spacetime(“bulk”) bulk IR UV

32. Holographic probes – local op • 1-point function boundaryoperator boundary bulk field UV IR perturbation vev 1-point function knows only about UV

33. Holographic probes – non-local op • 2-point function boundary geodesic IR UV Non-local ops. know also about IR

34. 2.1 Models & probes of thermalization

35. Models for holographic thermalization Initial cond? • Not clear how to implementinitial cond in bulk • Various scenarios • Collision of shock waves [Chesler+Yaffe]… • Falling string[Lin+Shuryak]… • Boundary perturbation [Bhattacharyya+Minwalla]… Thermalization BH formation

36. The bulk spacetime singularity AdS boundary event horizon AdSBH turn off pert. shock wave turn on pert. empty AdS UV IR

37. Probes of thermalization (1) • Instantaneous thermalization? • Inside = empty AdSOutside = AdS BH • 1-point functioninstantaneously thermalizes [Bhattacharyya+Minwalla] singularity 1-pt func:same as that in thermal state event horizon AdSBH turn off pert. shock wave turn on pert. empty AdS AdS boundary IR UV

38. Probes of thermalization (2) • Local operators are not sufficient • They know only about near-bndyregionThey probe UV only • Non-local operators do better job • They reach deeper into bulkThey probe IR also • They know more detailabout thermalization process local op non-localop AdS boundary IR UV

39. Non-local operators • 2-point function • Bulk: geodesic (1D) • Wilson line • Bulk: minimal surface (2D) • Entanglement entropy • Bulk: codim-2 hypersurface minimal surface geodesic bulk bulk AdS boundary AdS boundary Let’s study these during BH formation process!

40. 2.2 The model and results

41. The model: Vaidya AdS • Null infalling shock wave in AdS (Vaidya AdS spacetime) • Thin shell limit UV (AdS boundary) IR • Simple setup amenable to detailed study sudden, spatially homogen. injection of energy • Sudden & spatially homog. injection of energy • BH forms at late time • We study AdSDwith D=3,4,5 field theory in d=2,3,4

42. Nonlocal probes we consider

43. What we computed • AdS3 • Can be solved analytically in thin shell limitCf. Numerically done in [Abajo-Arastia+Aparicio+Lopez 1006.4090] • AdS4 • NumericalCf. Partly done in [Albash+Johnson 1008.3027] • AdS5 • Numerical

44. Geodesics in AdS3 (1) • Equal-time geodesics shock wave geodesic bulk AdS boundary • Geodesic connecting two boundary points at distance ,at time after energy was deposited into system • Refraction cond across shock wave

45. Geodesics in AdS3(2) • Analytic expression Equal-time geodesics for fixed and Equal-time geodesics for fixed and

46. Result: geodesic length AdS3 AdS4 AdS5 • Given fixed compute as function of • Renormalize by subtracting thermal value • If we wait long enough, (thermalize) • Larger It takes longer to thermalize ― “Top-down”

47. “Thermalization time” from geodesics AdS3 AdS4 AdS5 becomes equal to the thermal value : becomes half the thermal value has steepest slope • is as expected from causality bound • Others would indicate : superluminous propagation?? Should look at observable that gives largest

48. “Causality bound”

49. Other non-local observables CircularWilson loop RectangularWilson loop Entanglement Entropy AdS4 N/A AdS5 • Similar behavior for all probes – “Top-down” thermalization

50. Thermalization time circularWilson loop Rectangular Wilson loop EE fora sphere geodesic AdS3 N/A N/A N/A AdS4 N/A AdS5 • EE for disk/sphere saturates the causality bound • Infinite rectangle doesn’t have one scales – reason for larger ?