Transport properties of strongly coupled Quark-Gluon Plasma s

Transport properties of strongly coupled Quark-Gluon Plasma (s. QGP) Edward Shuryak Department of Physics and Astronomy State University of New York Stony Brook NY 11794 USA

Two types of transport particles <=> momentum (diffusion <=> viscosity) In gases both are proportional to the same collision cross section, but as coupling strength goes up in MD, Diffusion constant indefinitely decreases <= Particles ``get stuck” and cannot move Related to drag force By Einstein relation Dp/dx sim 1/D in. Ad. S/CFT Viscosity only decreases for a while, And then other means of momentum Trasfer -- via collective modes -- appears viscosity is again large And in glasses and solids at very strong coupling

Viscosity-diffusion summary plot ^ Better liquid Ad. S/CFT eta/s: Kovtun, Son, Starinets, hep-th/0405231 Dc: Casalderrey, Teaney, PRD 74, 085012 (06) Colored lines: Classical MD for a strongly Coupled plasma with Monopoles: Liao, ES hep-ph/0611131, v 2 (and this fig, is from its) w. CFT: eta: Huot et al hep-ph/0608062 Dc: Chesler and Vuirinen hepph/0607148 ==> particle gets less mobile Plasma coupled stronger

Why do we think that QGP is strongly coupled at RHIC? I-RHIC phenomenology • 1 a: hydro works => viscosity is very low: eta/s=. 1 -. 2 << 1 (Teaney, ES) • 1 b: Because parton cascade requires huge cross sections >> (p. QCD predictions) (Molnar-Gyulassy) (a comment: they are not the same => a cascade makes no sense in a strongly coupled regime, while hydro only works better) • 1 c: charm diffusion: Dc << p. QCD predicts (from R_AA and v 2 of electrons at RHIC <= Moore+Teaney) • 1 d: very strong jet quenching, including charm, again well beyond p. QCD predictions • 1 e: conical flow from quenched jets in Mach direction (Casalderrey-Teaney –ES) seem to be observed

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”

PHENIX jet pair distribution Note: it is only projection of a cone to asymuth Note 2: more recent data on 3 body correlators, from both STAR/PHENIX are consistent with conical flow , not a deflected jet

Why do we think that QGP is strongly coupled at RHIC? II-lattice+QM • 2 a: ``New spectroscopy”: Interaction is strong enough to make multiple bound states (ES+Zahed, 03), s-wave n=1 mesons, colored pairs like qg or non-singlet gg • 2 b: Marginal states with small binding may lead to small m. f. p. <= (ES+Zahed, 03) a la Feshbach resonances for ultracold trapped atoms –charmed (Rapp, van Hees) • 2 c: Baryons seem to survive till about 1. 6 Tc (Liao, ES) • 2 d: large energy (up to 4 Ge. V) and entropy (up to 20) of a heavy dipole around Tc (Karsch et al, 04) remains a mystery: huge number of states, many quasiparticles? Protostrings =>Polymeric “electric” chains of gluons bar. Q - g … Q (Liao, ES)

Why do we think that QGP is strongly coupled at RHIC? III: Ad. S/CFT N=4 SUSY YM theory at strong coupling at finite T s. QGP at RHIC • 3 a: p, e=O( N^2 T^4) even the famous coefficient. 8 is better reproduced by the large-g (Klebanov… 96) series (3/4+…) • 3 b: viscosity is small: eta/s=1/4 pi (Son et al, 04) • 3 c: Heavy quark drag and diffusion constant are OK (Yaffe et al, Casalderrey-Teaney) (Gubser et al) and conical flow is seen a complete gravity dual to RHIC collisions => departing black hole/ horizon=>ES, Sin+Zahed, Janik-Peschanski, Gubser… • 3 e: quasiparticles are heavy M*=sqrt(lambda)T>>T and have • 3 d: huge number of bound states

Why do we think that QGP is strongly coupled at RHIC? IV-Electric/Magnetic duality • N=2 SUSY YM (``Seiberg-Witten theory”) is a working example of confinement due to condenced monopoles • It teached us that monopoles must be very light and weakly interacting (in IR) near the critical point • This + Dirac condition => [(e g)/hbar c=1/2] => electric coupling must be large there • e/m equilibrium at (1. 2 -1. 5)Tc: gluons and monopoles have comparable masses and couplings => • New picture: s. QGP is a plasma of fighting electric and magnetic quasiparticles

New (compactified) phase diagram describing an electric-vs-magnetic fight Dirac condition Thus at the e=g line Near deconfinement line g->0 in IR (Landau’s U(1) asymptotic freedom) => e-strong-coupling Why this diagram is better? => in all blue region There are e-flux tubes, not only in the confined phase! In fact, they are maximally enhanced at Tc, not below it.

Entropy (and energy) associated with a static dipole gets huge at Tc (shown at large r only vs T/Tc ) • #(states) =exp(S)=e^16 What those states may be? • string picture provides the answer (Polyakov 78 => Klebanov, Maldacena, Thorn et al hep- th/0602255) • EQP language: electric polymers (Liao, ES hep-ph/0508035 Ads/CFT Minahan 98) Kaczmarec et al hep-lat/0510094

are there e-flux tubes in QGP? • Dual superconductivity as a confinement mechanism (‘t. Hooft, Mandelstam 1980’s) => monopole condensation at T Meissner effect confines electric fluxes (dual to Abrikosov vortices) • But at T>Tc (uncondenced) MQPs do the same! Due to Lorentz force they are reflected from a region with E field => compressing into flux tubes, even in classical plasma! E

magnetic flux tubes at the Sun, (work without any superconductor!) where classical electrons rotate around it • B: about 1 k. G, • Lifetime: few months

Electric and magnetic screening masses E/M equilibrium Dual Superconductor model works well • vacuum with monopole condensate • flux tube as Abrikosov vortex • Seiberg-Witten, a working example E dominated Mdomi nated A. Nakamura, et al, PRD 69(2004)014506 G. S. Bali, hep-ph/9809351 Approaching Tc from above: • E-screening mass decrease less E-charge getting heavier • M-screening mass increase more M-charge getting lighter

Classical strongly coupled plasmas As Gamma= <|Epot|>/ grows gas => liquid => solid Gelman, ES, Z ahed, nuclth/0601029 With a non-Abelian color => Wong eqn Gas, liquid solid

MD simulation for plasma with monopoles (Liao, ES hep-ph/0611131) monopole admixture matters: 50 -50 mixture makes the best liquid diffusion decreases indefinitely, viscosity does not (1000 particles in a stable spherical drop) Diffusion can be stopped

A flurry of recent papers on heavy quark dynamics in N=4 plasma • HKKKY hep-th/0605158 • J. Casalderrey and D. Teaney hep-ph/0605199 diffusion constant for heavy quark • Agree nicely via Einstein relation (very nontrivial in string setting) • Qualitatively agree with classical MD results!

Now we compare Dc to weak and strong coupling predictions ==> Range from MD With different EQPs/MQPs ratio ==> Strong: not very Diferent from MD The cross is phenomenological range added by me, following Moore-Teaney R_AA, v 2 Weak coupling Chester and Vuorinen, Hep-ph/0607148

Floating matter destribution Friess et al, 0607022

Subsonic emission => no cone (as in b-tagged jets – Antinori, ES, nucl-th/0507046) subsonic Supersonic Note how angle moves as v ->cs

Short history of developing ``gravity dual” for RHIC from basically 5 dim GR • Ad. S+Black Hole: Hawking radiation from the horizon is used to mimic non-zero T (Witten, 98) • receeding BH/horizon from collapsing matter =>cooling+expansion (ES, Sin, Zahed, 05) • Stretching black hole => Large-time solution (Janik-Peschanski, 05) reproduces Bjorken hydro, even with viscosity (Nakamura+Sin, 06, Janik 06) • Falling objects produced in a collision form a membrane falling under its own weight => (Shu Lin and ES, hep-ph/0610168) <= Israel’s junction cond. 1966 • nov. 06 Gubser et al Departing point black hole solution => spherically expoding fireballl

(Shu Lin and ES, hep-ph/0610168) Ad. S 5 center departing 2 heavy ultrarelativistic quarks stretch a longitudinal string 5 -dim Pythia model in which strings don’t break But fall instead into the 5 th dimension Scaling solution (used in Euclidean appl. By Gross et al, is only stable if Y<. 27 and exist if Y<. 5 Makeenko) Ad. S 5 center The non-scaling solution approach rectangular shape, small fragmentation region and rapidity-independent bulk

All objects – massless, massive close strings, open strings => fall in Ad. S and form a massive membrane because they tend to the same trajectory at large time => Observer at z=0 (r=infty) sees induced Tmn with hydro flow Strething black hole has approximately conserved horizon area => entropy Old Ad. S metric New metric, JP at late time (I disagree with Janik on singularity issue)

n Conclusions Strongly coupled QGP has been produced at RHIC n robust collective flows, even for charm n Strong jet quenching leading to robust conical flow, n now supported by 3 body correlators at (1 -1. 4)Tc dominated by magnetic QPs n postconfinement with e-flux tubes n Ad. S/CFT => strongly coupled conformal regime not too close to Tc Heavy quark diffusion and quenching in the right ballpark conical flow seen • Classical MD n hydro explosion can be derived from GR is being done, => smaller Collapsing membrane, bh viscosity due formation to monopoles