Understanding strongly coupled quarkgluon plasma the tale of

Understanding strongly coupled quark-gluon plasma (the tale of two dualities) (year-end 2008 theory meeting, Durham) Edward Shuryak Stony Brook

l RHIC: collective flows and jet quenching Why is quark-gluon plasma (s. QGP) at RHIC such a good liquid? q QGP and e/m duality: magnetic plasma near Tc § Lattice confirmations of the magnetic scenario The trapping via magnetic bottle effect q q molecular dynamics (MD) of Non-Abelian plasma with monopoles(B. Gelman, I. Zahed, ES, PRC 74, 044908, 044909 (2006), J. F. Liao, ES, hep-ph/0611131, PRC 07): q Quantum gluon-monopole scattering (Ratti +ES, 08) Ad. S/CFT duality vs RHIC results q q q q Viscosity and diffusion constant from Ad. S/CFT, New meaning of dissipation: falling waves, strings, ``stones” Few holograms: from Maldacena dipole to conical flow ``membrane paradigm” and derivation of hydro equilibration=the black hole formation , entropy and trapped surfaces transport summary; both dualities -Ad. S/CFT and s. QGP with monopoles - seem to work. Summary: How are two dualities related? ? ? LHC ?

Main RHIC findings l Strong radial and elliptic flows are very well described by ideal hydro => ``the most perfect liquid known” l Strong jet quenching, well beyond p. QCD gluon radiation rate, same for heavy charm quarks (b coming) l Jets destroyed and their energy goes into hydrodynamical ``conical flow”

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 s 1/4 • 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…}

My hydro history • Hydro for e+e- as a spherical explosion PLB 34 (1971) 509 => killed by discovery of the asymptotic freedom and 1976 discovery of jets in e+e • Looking for transverse flow at ISR in pp: ES+Zhirov, PLB (1979) 253 =>Killed by apparent absence of transverse flow in pp ES+Hung, prc 57 (1998) 1891, radial flow at Pb. Pb at CERN SPS with correct freezeout surface worked!

views on QGP in 1970’s • OK, p. QCD and weak coupling at small distances…but at large ones the coupling gets strong! => makes the QCD vacuum so compicated… (instantons, monopoles, vortices and other beasts live there) Can one measure the nonperturbative vacuum pressure/energy density, the so called ``true” bag constant ?

From Magdeburg hemispheres (1656) and dreams of 1970’s to RHIC (2000) • “We cannot pump out complicated objects populating the QCD vacuum, but we can pump in something else, namely the Quark-Gluon Plasma, and measure in the explosion the pressure difference” => p(QGP)-p(vacuum) (QGP in 1970’s was viewed as a simple near-ideal quark-gluon gas, just ``needed to fill the bag”)

One may have an absolutely correct asymptotic theory and still make accidental discoveries… Columbus believed if he goes west he should eventually come to India But something else was on the way… We believed if we increase the energy density, we should eventually get weakly interacting QGP. But something else was found on the way, s. QGP

Contrary to expectations of most, hydrodynamics does work at RHIC! Elliptic flow How does the system respond to initial spatial anisotropy? is it macro or microscopic? )

The coolest thing on Earth, T=10 n. K or 10^(-12) e. V can actually produce a Micro -Bang ! (J. Thomas et al, Duke ) Elliptic flow with ultracold trapped Li 6 atoms, a=> infinity regime The system is extremely dilute, but can be put into a hydro regime, with an elliptic flow, if it is specially tuned into a strong coupling regime via the so called Feshbach resonance

2001 -2005: hydro describes radial and elliptic flows for all secondaries , pt<2 Ge. V, centralities, rapidities, A (Cu, Au)… Experimentalists were very sceptical but were convinced and ``near-perfect liquid” is now official, =>AIP declared this to be discovery #1 of 2005 in physics proton v_2=<cos(2 phi)> pion PHENIX, Nucl-ex/0410003 red lines are for ES+Lauret+Teaney done before RHIC data, never changed or fitted, describes SPS data as well! It does so because of the correct hadronic matter /freezout via hadronic cascade(RQMD)

So it is even less than presumed Lower bound (Son et al) >1/4 ! Why it may be possible, read Lublinsky, ES hep-ph 0704. 1647

Jet quenching (disappearence)

Sonic boom from quenched jets Casalderrey, 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 Wake effect or “sonic boom”

Two hydro modes can be excited (from our linearized hydro solution): a ``diffuson” a sound

PHENIX jet pair distribution Mach angle The most peripheral bin, here there is no QGP, thus the usual 2 jets

One more surprise from RHIC: strong jet quenching and flow of heavy quarks nucl-ex/0611018 Heavy quark quenching as strong as for light gluon-q jets! Radiative energy loss only fails to reproduce v 2 HF. Heavy quark elliptic flow: v 2 HF(pt<2 Ge. V) is about the same as for all hadrons! => Small relaxation time t or diffusion coefficient DHQ inferred for charm.

Electric/magnetic duality explains transport in s. QGP plasma becomes magnetic near Tc (monopoles and dyons take the place of quarks and gluons) Unexpected properties

Magnetic objects and their dynamics: classics ‘t Hooft and Polyakov discovered monopoles in Non-Abelian gauge theories l ‘t Hooft and Mandelstamm suggested “dual superconductor” mechanism for confinement l Seiberg and Witten shown that it does work in N=2 Super Yang. Mills theory l

Recent developments l Liao+ES 06; oppositely running couplings => magnetic liquid near Tc, flux tubes, l Chernodub+Zakharov 06=> high monopole density near Tc, e-3 p from monopoles l D’Ellia+D’Alessandro 07, 08=> monopole density and spatial correlators l Liao+ES 08 =>correlators are the same as in the Coulombic plasma in a liquid form l Ratti+ES 08: gluon-monopole quantum scattering

Metastable flux tubes…

Electric and magnetic screening from the lattice Nakamura et al, 2004 arrow shows the ``self-dual” E=M point Me<Mm Magnetic Dominated At T=0 magnetic Screening mass Is about 2 Ge. V (de Forcrand et al) (a glueball mass) (Other lattice data -Karsch et alshow Me Vanishes at Tc better) Me>Mm Electrric dominated ME/T=O(g) ES 78 MM/T=O(g^2) Polyakov 79 Why is QGP getting magnetic as T=>Tc?

• • Strong coupling regime in plasma physics: Gamma= <|Epot|>/<Ekin> >>1 gas => liquid => solid Strongly compressed matter inside Jupiter etc when electrons gets collective ``dusty plasmas’ at International Space Station This is of course for +/Abelian charges, But ``green” and ``antigreen” quarks do the same! • local order would be preserved in a liquid also, as it is in molten solts (strongly coupled TCP with <pot>/<kin>=O(60), about 3 -10 in s. QGP)

Gelman, ES, Zahed, nuclth/0601029 With a non-Abelian color => Wong eqn Gas, liquid solid

Our MD for 50 -50 MQP/EQP

s(electric) and s(magnetic) do run in opposite directions! • Squares: fitted magnetic coupling, circles: its inverse compared to asymptotic freedom (dashed) • Effective plasma parameter (here for magnetic) • So, the monopoles are never really weakly coupled!

We found that two charges play pingpong by a monopole without even moving! Chaotic, regular and escape trajectories for a monopole, all different in initial condition by 1/1000 only! Dual to Budker’s magnetic bottle

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

short transport summary log(inverse viscosity s/eta)- vs. log(inverse heavy q diffusion const D*2 pi. T) (avoids messy discussion of couplings) ->Stronger coupled -> • RHIC data: very small viscosity and diffusion • vs theory Ad. S/CFT and our MD Most perfect liquid 4 pi 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

• Quantum problem of gluon-monopole scattering • n=eg (=1) is the only parameter, if we ignore the monopole core and keep only Coulomb B field j’ is not an integer!

A surprize: no corrections to thermodynamics • Beth-Uhlenbeck correction (extra states in a box) is zero because there is no dependence on k

Scattering amplitude vs maximal impact parameter or jmax

Not surprising, large correction to transport • RHIC: T/Tc<2, LHC T/Tc<4: we predict hydro will still be there, with h/s about. 2

Ad. S/CFT duality from weakly coupled(super)gravity in Ad. S 5 to strongly coupled CFT (N=4 SYM) plasma what LHC people dream about -- a black hole formation -does happen, in each and every RHIC Au. Au event ! What we see at RHIC is a hologramm of this process…

The first gauge-string duality Ad. S/CFT, found in 1997! l Ad. S/CFT correpondence or ``Maldacena duality” was found on the long path illuminated by Witten, Polyakov, Polchinski, Klebanov…

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

A hologramm of a dipole in a stronly coupled vacuum: not just dielectric constant and not even only electric E! • Shu Lin, ES ar. Xiv: 0707. 3135 recently evaluated holographic stress tensor from the Maldacena string Here is large r behavior: • T 00 =>(g 2 N)1/2 d 3/r 7 times function of the angle plotted by a solid line (to be compared to zero coupling, the dashed line, also to (g 2 N)d 2/r 6 ) Short time of color correlation t=d/sqrt(lambda) (ES, Zahed 03, Klebanov, Maldacena, Thorn 05)

Heavy quark diffusion J. Casalderrey+ D. Teaney, hep-ph/0605199, hep-th/0701123 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

subsonic supersonic Left: P. Chesler, L. Yaffe Up- from Gubser et al Both Princeton and Seattle groups made amasingly detailed description of the conical flow from Ad. S/CFT=> excellent agreement with hydro

Membrane paradigm and new derivation of hydro:

Equilibration and “gravity dual” • From cold T=0 (extreme BH= mass is minimal for its charge => no horizon Ad. S ) 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, • Bjorken flow: BH longitudinally stratching (Janik-Peschanski 05) proposed late- • • d=1, 2, 3 collapses, ( Sin, ES and Zahed 04) time solution, Sin, Nakamura, Janik -viscosity role, Heller 08) 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) • Falling membrane (Lin+ES, 08) • Entropy formation and trapped surfaces (Gubser, Pufu, Yarom 08)

Gravity dual to the (e+e-=>heavy quarks) collision: “Lund model” in Ad. S/CFT (Shu Lin, ES, I+II papers ) If colliding objects are made of heavy quarks • Stretching strings are falling under the Ad. S gravity and don’t break • Instability of simple scaling solution and numerical studies • Analogs of longitudinal E, B in w. GLASMA Ad. S 5 center= Extremal b. h.

• Holographic image of a falling string 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” T 00 , Toi

• Falling is dual to further equilibration UV=>IR

Israel junction condition is dual to the equilibration dynamics • Thermal Ad. S above= fully equilibrated • Cold Ad. S 5 below= not equilibrated

Average Tmunu is thermal but Correlators (measured by the two-point observers) deviate from equilibrium The reason for oscillations in spectral densities is in fact the ``echo” effect, induced by a gravitons scattering from a membrane, Confirmed numerically and semiclassically

Entropy production from first estimates of area of trapped surface • • Power= (D-3)/(D-2) Gubser, Pufu, Yarom” Heavy ion collisions as that of two black holes

From RHIC to LHC: (no answers, only 1 bn$ questions: I don’t mean the price of LHC, of course, but only of heavy ion detector ALICE) l Will ``perfect liquid” be still there? l Is jet quenching as strong, especially for c, b quark jets and much larger pt? l Is matter response (conical flow at Mach angle) similar? (This is most sensitive to viscosity…)

From SPS to LHC • lifetime of QGP phase nearly doubles, but v 2 grows only a little, to a universal value corresponding to Eo. S p=(1/3)epsilon • radial flow grows by about 20% => less mixed / hadronic phase (only 33% increase in collision numbers of hadronic phase in spite of larger multiplicity) (hydro above From Nonaka/Bass)

Conclusions Strongly coupled QGP is produced at RHIC T=(1 -2)Tc l This is the region where transition from magnetic to electric dominance happen l at T<1. 4 Tc magnetic objects dominate => l l. Good liquid Ad. S/CFT => natural l Ad. S/CFT => natural because of applications of string magnetictheory, N=4 SYM is not QCD: nonconfining and bottle Strongly coupled, s. QGP is OK trapping Equilibration=black hole l. Classical MD formation is being l RHIC data on transport done, the (eta, D), ADS/CFT and lowest viscosity classical MD all for 50 -50% qualitatively agree! electric/magnet ic plasma l Are these two l. Quantum gm scattering nontrivial l dualities related?

reserve

The monopole density (vs T/Tc) in confined and deconfined phases • The zero T: lattice, Ilgenfritz et al • Near-Tc: condenced and uncondenced monopoles, from flux tubes (Liao ES) • The solid line represent the density of gluons

viscosity from Ad. S/CFT (Polikastro, Son, Starinets 03) Kubo formula <Tij(x)Tij(y)>=> • • • Left vertical line is Ad. S boundary (our 4 d Universe, x, y are on it) Temperature is given by position of a horizon • T=T(Hawking radiation) (Witten 98) graviton propagator G(x, y) dual to sound • Blue graviton path does not contribute to Im G, but the red graviton path (on which it is absorbed) does Both viscosity and entropy are proportional to b. h. horizon, thus such a simple asnwer

Effective coupling is large! alphas=O(1/2 -1) (not <0. 3 as in p. QCD applications) t. Hooft lambda=g 2 Nc=4 pi. Nc=O(20)>>1 -1 Bielefeld-BNL lattice group: Karsch et al