Strongly coupled QGP: New Frontiers

1. Strongly coupled QGP: New Frontiers (Quark Matter 2008, Jaipur India) Edward Shuryak Stony Brook

2. Experimental frontiers(not to be discussed) • High energy: LHC Will ``perfect liquid” be still there? • High luminocity at RHIC • Low energy/high barion density: RHIC/lowS,NA61 and Fair/GSI => the critical and the “softest” points

3. Prologue: multiple views on sQGP (which forced us to learn a lot in the last few years…) Quantum mechanics Stronly coupled cold trapped Atoms: 2nd best liquid Manybody theory Lattice simulations sQGP Quasiparticles Potentials correlators Bound states of EQP and MQP J/psi,mesons,baryons,calorons Bose-Einstein Condensation -> confinement EoS Flux tubes-> RHIC data Hydrodynamics Molecular dynamics Monopoles Transport properties, Entropy generation Plasma physics E/M duality Collective modes Energy loss, Mach cones AdS/CFT duality Gauge theories, SUSY models Black hole physics, String theory

4. Fundamental questions (answers?) • What is the dynamics of confinement/deconfinement? (-) • What are the magnitude and T-dependence of electric and magnetic couplings in sQGP? What are the masses and the role of magnetically charged quasiparticles in sQGP? (+-) • Why is quark-gluon plasma (sQGP) at RHIC such a good liquid? (small /s, TDc ,large dp/dt) (++) • Is it only true in the RHIC domain T=(1-2)Tc? Will we see sQGP signals at LHC as well? (--) • AdS/CFT equilibrium results eta/s, jet quenching, conical flow, photon emission. Can one obtain a complete “gravity dual to RHIC” including equilibration/entropy?(+) • Can we even qualitatively understand AdS/CFT results without duality? (--)

5. outline • A bit of hydro • Electric-magnetic duality(fight,competition…) • Gauge-string duality - AdS/CFT • Out of equilibium: sGlasma=>sQGP • conclusions

6. Thermo and hydrodynamics: can they be used at sub-fm scale? • Here are three people who asked this question first: • Fermi (1951) proposed strong interaction leading to equilibration: <n>about s1/4 • Pomeranchuck (1952) introduced freezeout • Landau (1953) explained that one should use hydro in between, saving Fermi’s prediction via entropy conservation{he also suggested it should work because coupling runs to strong at small distance! No asymptotic freedom yet in 1950’s…}

7. My own hydro history • Hydro for e+e- as a spherical explosion: PLB 34 (1971) 509 => killed in 1973 by as.freedom and in 1976 by SLAC discovery of jets in e+e- • Looking for it in pp: transverse flow at ISR, ES+Zhirov, PLB (1979) 253 =>Killed by apparent absence of transverse flow in pp • ES+Hung, prc57 (1998) 1891, radial flow at PbPb at CERN SPS worked (but only with correct differential freezeout surfaces!)

8. main RHIC finding: Strong radial and elliptic flows are very well described by ideal hydro 2001-2002: hydro describes radial and elliptic flows for all secondaries , pt<2GeV, centralities, rapidities, A (Cu,Au)… Most theorists/experimentalists were very sceptical but were eventially convinced and the term picked up by D.Teaney and myself in 2003 => ``the most perfect liquid known” gets official=>AIP declared this to be discovery #1 of 2005 in physics • Jets destroyed and their energy goes into hydrodynamical ``conical flow” H.Stocker 04,Casalderrey,ES,Teaney 04…. Btw, Mach cone ideas of 1970’s did not work because nucleai Are not such perfect liquid as sQGP…

9. So it may be even less than Famous 1/4!

10. Corrections are small for such eta/s • Especially at final/later time • v2(pt) is changing at the tail and improves • Agreement at pt>1 GeV • But (my comment) relying on small tails • is dangerous

11. D.Molnar talk here sQGP is not a Gas => Boltsmann Approach inapplicable Yet it can be used with subdivisions as a model

12. As effect of viscosity is small O(10%), thus all other uncertainties have to be included: initial deformation shown by Raju, but one has to deal with ALL of them • Color glass produces a bit different initial shape with sharper edge • Include fluctuations (crucial at large b) • Time to do UU collisions? ES,nucl-th/9906062,Bao-An Linucl-th/9910030 Heinz, Kuhlmannucl-th/041105

13. 4/s<1? Generalized viscosity from AdS/CFT (sound) decreases with k/T, (although we don’t know why) M.Lublinsky+ES, hep-ph0704.1647 PRC ,and in progress 4/s(k/2T,/2 T) Im and Re Note reduction of Re at larger k/2T Elliptic flow forms early, for peripheral collisions the almond is thin enough that this effect may play a role: again larger deformed systems needed

14. Deconfinement and Electric-magnetic fight/competition in sQGP . Magnetic quasiparticles -- monopoles and dyons -- are important/dominant at T< 1.5Tc This affect thermodynamics and especiallytransport due to nontrivial“magnetic bottle” effect

15. Magnetic objects and their dynamics: classics • ‘t Hooft and Polyakov discovered monopoles in YM gauge theories • ‘t Hooft and Mandelstamm suggested dual superconductor mechanism for confinement • Seiberg and Witten shown that it does work in N=2 SYM

16. Liao,ES hep-ph/0611131 electric/magnetic couplings (e/g) must run in the opposite directions! Old good Dirac condition (in QED-type units e2= s) n=2 (Higgs A0) s(el)s(mag)=1 s(el) at the e=g “equilibrium line” s(el)=s(mag)=1 (the best liquid here?) s(mag) Near deconfinement line monopoles much lighter than gluons/quarks =>s(mag) small (Landau pole) => So s(el)must be strong!

17. Electric and magnetic scrreningMasses, Nakamura et al, 2004My arrow shows the ``self-dual” E=M point Me<Mm Magnetic Dominated At T=0 magnetic Screening mass Is about 2 GeV (de Forcrand et al) (a glueball mass) (Other lattice data -Karsch et al- show how Me Vanishes at Tc better) Me>Mm Electrric dominated ME/T=O(g) ES 78 MM/T=O(g^2) Polyakov 79

18. x-Correlations give MM potential (Mag.length only .1 fm!) +- monopole density strongly grows as T=> Tc ++

19. Very recent data (thanks to M.D’Elia)confirm that correlation strength increases with T, indeed opposite to electric So at least the magnetic coupling does behave as Landau thought

20. Understanding monopole dynamics • Claudia Ratti+ES: Higgsing<L(T)> for g,q, tHooft-Polyakov monopoles +lattice data (e.g n(mon,T)) =>masses of q,g,m and s(el,T),s(mag,T) • Electric Flux Tubes in Magnetic Plasma.Jinfeng Liao+ES arXiv:0706.4465 derives conditions for (meta) stable flux tubes at T>Tc and explains lattice data on static potentials • Marco Cristoforetti +ES: Bose-condensation in strongly interacting liquids => Monopole mass at Tc from Feynman condition

21. Bose-Einstein condensation of strongly interacting particles(with M.Cristoforetti,now TU Munich) • Feynman theory polygon jumps BEC if ∆S(jump)<Sc=1.65-1.8 d • We calculated ``instantons” for particles jumping paths in a liquid and • solid He4 incuding realistic atomic potentials and confirmed it semiclassically • Marco is doing Path Integral simulations with permutations numerically, to refine conditions when BEC transitions take place • BEC (confinement) for monopoles • the action calculated relativistically • ∆S=M sqrt(d2+(1/Tc)2) = Sc • => M(mon, T= Tc)=O(300 MeV) << M(g,q)=O(800 MeV) Jumping paths: Feynman, interacting and interacting weakly

22. So why is such plasma a good liquid? Because of magnetic-bottle trapping: static eDipole+MPS Note that Lorentz force is O(v)! + E+ M V E- - Monopole rotates around the electric field line, bouncing off both charges (whatever the sign)

23. Note that collisions are much more frequent than in cascades We found that two chargesplay ping-pong by a monopole without even moving! Dual to Budker’s magnetic bottle

24. MD simulation for plasma with monopoles (Liao,ES hep-ph/0611131)monopole admixture M50=50% etcagain diffusion decreases indefinitely, viscosity does not It matters: 50-50 mixture makes the best liquid, as it creates ``maximal trapping”

25. AdS/CFTdualityfrom gravity in AdS5 to strongly coupled CFT (N=4 SYM) plasma (LHC people dream about a black hole formation -- But it does happen, in each and every RHIC AuAu event but in the 5th direction!What we see at RHIC is its 4d hologram…)

26. The first gauge-string duality AdS/CFT, found in 1997! • AdS/CFT correpondence or ``Maldacena duality” was found on the long path illuminated by Witten, Polyakov, Polchinski, Klebanov… • (not so dangerous as Larry McLerran thinks)

27. How can it help us? • T=0 setting and the first example of a hologram • T nonzero: eta/s, Dc or dp/dt, conical flow as the second hologram • sQLASMA (out of equilibrium): gravity dual for RHIC, t-dependent hologram of a falling string, making the entropy

28. The duality setting • CFT (conformal gauge theory)N=4 SYM a cousin of QCD (chromodynamics=theory of strong interaction) in which the coupling =g2Nc does not run. • It lives on flat 4-dim boundary of 5-d curved AdS (anti-de-Sitter) space where weakly coupled(super)gravity is a description of (super) string theory • Strategy: calculate in the “bulk”, then project on the boundary • Hint; think of extra dimension as a complex variable trick: instead of functions on the real axes one may think of poles in a complex plane

29. The 5th coordinate • the 5th coordinate z, dim=length=1/momentum • its physical meaning is a ``scale” as in renorm.group • z=>0 is ``high scale” UV or very high energies, z=>infinity is low scale or IR • ds2 =(-dt2+dx12 +dx22 +dx32 +dz2)/z2 so distances in z are logarithmic. Light speed is still 1 in all directions • z=L2/r where r is distance from b.h. => Gravity force is acting toward large z, “stones” fall there • (unless they are BPS states which levitate --Newton cancels Coulomb) • AdS/QCD with running coupling g(z): strong in some region only (Kiritsis et al,07, also my recent proposal of 2 domain scenario ES,07)

30. Maldacena’s dipoleThe Coulomb law at strong coupling • Maldacena,Rey,Yee -98 one of the first apps: • The string (=flux tube) is pending and has a minimal action • Modified: at strong coupling, (g2N)1/2 << (g2N) because of short-time color correlations ES+Zahed,04 • Can it be just a factor, like a dielectric constant? z

31. A hologramm of a dipole in a stronly coupled vacuum: not just dielectric constant and not even only electric E! • Shu Lin,ES arXiv:0707.3135 recently evaluated holographic stress tensor from the Maldacena string Here is large r behavior: • T00 =>(g2N)1/2d3/r7 Times function of the Angle which is plotted by a solid line (to be compared to zero coupling =>(g2N)d2/r6 Times another function (dashed)

32. viscosity from AdS/CFT(Polikastro,Son, Starinets 03) • T is given by position of a horizon (Witten 98) of non-extreme b.h. • Kubo formula <Tij(x)Tij(y)> => graviton propagator G(x,y) Both viscosity and entropy are proportional to area of b.h. horizon • Horizon not only has Hawking T and Bekenstein S, but many other universal properties:T.Damour (1982) => electric conductivity, shear and bulk viscosity • K.Thorne et al (1980s) put it in the “membrane paradigm” form in which many astrophysical problems were solved • (e.g. planets rotating around and plunging into B.H., accretion discs with magnetic and electric fields, thermal atmospheres etc) • => “dissipation is at the bottom” since horizon membrane is black

33. Heavy quark diffusion J.Casalderrey+ D.Teaney,hep-ph/0605199,hep-th/0701123 W O R L D One quark (fisherman) is In our world, The other (fish) in Antiworld (=conj.amplitude) String connects them and conduct waves in one direction through the black hole A N T I W O R L D

34. subsonic supersonic Left: P.Chesler,L.Yaffe Up- from Gubser et al Both groups made Amasingly detailed Description of the conical flow from AdS/CFT=>very close to hydro but corrections can be inferred

35. Related to talk by Iancu here Photon spectrum has a different shape in sQGP: bremmstrahlung is strongly suppressed while hard photons are enhanced wQGP sQGP

36. short transport summarylog(inverse viscosity s/eta)- vs. log(inverse heavy q diffusion const D*2piT) (avoids messy discussion of couplings) ->Stronger coupled -> • RHIC data: very small viscosity and diffusion • vs theory - AdS/CFT and our MD Most perfect liquid 4pi MD results, with specified monopole fraction Weak coupling end => (Perturbative results shown here) Both related to mean free path 50-50% E/M is the most ideal liquid

37. Non-equilibrium “gravity dual” => sGLASMA • From cold T=0(extreme BH= mass is minimal for its charge => no horizon AdS ) to hot non-extreme BH with a horizon => T • extra mass from collision created falling strings:Advantages: naturally dissipative+classical+produce correct Bekenstein entropy S • Expanding/cooling fireball= departing b.h. horizon in different geometries: 1+d, d=1,2,3 collapses, ( Sin,ES and Zahed 04) • Bjorken flow: BH longitudinally stratching (Janik-Peschanski 05) proposed late-time solution, Sin,Nakamura,Janik -viscosity role) • Spherical non-dissipative explosion Big Bang=1+3 departing BH, (Sin,ES and Zahed 04, in ADS Horowitz,Itzhaki,99, Gubser et al, 06) • non-dissipative explosion in 1+1 dim: (Kajantie et al 07)

38. Gravity dual to the (e+e-=>heavy quarks) collision: “Lund model” in AdS/CFT(Shu Lin,ES, I+II papers ) If colliding objects are made of heavy quarks • Stretching strings are falling under the AdS gravity and don’t break • Instability of simple scaling solution and numerical studies • Analogs of longitudinal E,B in wGLASMA AdS5 center= Extremal b.h.

39. a ``holographic image” of this process, • <= time-dependent Green function for linearized Einstein eqns How does it look for a falling string? Is it hydro-like explosion or not?

40. T00 , Toi • Holographic image of a falling string shows an explosion • (as far as we know the first time-dependent hologramm) • Which however cannot be reprensented as hydro fluid! => anisotropic pressure in the ``comoving frame” • (like in Raju’s wGLASMA)

41. The story of two membranes:(Many strings falling together) • Imagine 2 walls of heavy quarks => multiple strings falling (e.g.no dependence on transverse coordinates x2,x3) • The falling object is thus not a string but 3d membrane (or fabric) to be called Mm(for matter) • => another (more famous) membraneMh, (of the “membrane paradigm”) is hovering just above the horizon

42. The story of two membranes II(textbook example) • A thin spherical shell of massless “photons” falls radially and horizon is created • This is in global coordinates: distant observer (we need for AdS/CFT holography) does not see the b.h. interior Curvature at membrane jumps => Israel junction condition

43. Before equilibration The story of two membranes III(textbook example) • the stretching and falling “matter membrane”Mm, its ends have +/- v • horizon membraneMh bulges upward due to gravity of Mm till they merge • Fragmentation regions remain non-thermal but in the middle Mm gets substituted by Mh, • observer at midrapidity sees hydrodynamical hologram, but not in fragmentation regions

44. The horizon membrane can change shape easily provided its area (=entropy) is preserved as soap film • Mh is 3-dimensional in 5d, if stretched longitudinally a la Hubble x=vt, it moves in z=O(t1/3)=1/r so A=4S= O(x r3)=const (Janik et al) • In the next to leading order (in powers of inverse time) there is dissipation induced by the Mh viscosity

45. Questions to think about • Is this “two membrane paradigm” a AdS/CFT analog to top-down + down-up cascades? (collisional and bremmstrahlung equilibration) • Are instabilities/excitation of falling strings analogs of plasma instabilities (filamentation)? Unruh T? • How exactly flling strings get exactly the Bekenstein entropy?

46. Stronglycoupled QGP produced at RHIC is at T=(1-2)Tc => This is the region where electric/magnetic couplings cross AdS/CFT => natural applications to sQGP. In equilibrium almost done (but not understood) RHIC data on transport (eta/s,D), ADS/CFT and electric/magnetic QGP qualitatively agree! Are these two pictures related? LHC will tell Conclusions • Non-equilibrium time-dependent • AdS/CFT = sGLASMA • Two-membranes paradigm =>horizon provides T • Equilibration/entropy production in sQGP can benefit from 30 years or work on gravitational collapse+30 years of string theory • This makes so “perfect liquid” because of the magnetic-bottle trapping • the lowest viscosity for 50-50% electric/magnetic plasma

47. Thank you, Indian friends! Good by, Quark Matter 2008, Jaipur India

48. reserve

49. Wake effect or “sonic boom” Sonic boom from quenched jetsCasalderrey,ES,Teaney, hep-ph/0410067; H.Stocker… • the energy deposited by jets into liquid-like strongly coupled QGP must go into conical shock waves • We solved relativistic hydrodynamics and got the flow picture • If there are start and end points, there are two spheres and a cone tangent to both

50. Effective coupling is large! alphas=O(1/2-1) (not <0.3 as in pQCD applications)tHooft lambda=g2Nc=4piNc=O(20)>>1-1 Bielefeld-BNL lattice group: Karsch et al