Transport properties ofTransport properties of strongly coupled Quark-strongly coupled Quark-Gluon PlasmaGluon Plasma (sQGP) (sQGP)

Edward ShuryakEdward ShuryakDepartment of Physics and AstronomyDepartment of Physics and Astronomy

State University of New YorkState University of New York

Stony Brook NY 11794 USAStony Brook NY 11794 USA

Two types of transportparticles <=> momentum(diffusion <=> viscosity)

as coupling strength goes up in MD, inAdS/CFT

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Γ=<U > /T

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λ =g^2Nc

Diffusion constant indefinitely decreases <=

Particles ``get stuck” and cannot moveRelated to drag forceBy Einstein relationDp/dx \sim 1/D

Viscosity only decreases for a while,And then other means of momentum Trasfer -- via collective modes -- appears

And viscosity is again large in glasses and solids at very strong coupling

In gases both are proportional to the same collision cross section, but

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< x^2 >= (1/6)Dτ

Viscosity-diffusion summary plot

wCFT: eta:Huot et al hep-ph/0608062Dc:Chesler and Vuirinen hep-ph/0607148

AdS/CFTeta/s: Kovtun,Son,Starinets,hep-th/0405231Dc:Casalderrey, Teaney,PRD 74,085012 (06)

Colored lines:Classical MD for a strongly Coupled plasma with Monopoles: Liao,ES hep-ph/0611131,v2(and this fig, is from its)

==> particle gets less mobilePlasma coupled stronger

^Betterliquid

Why do we think that QGP is strongly

coupled at RHIC? I-RHIC phenomenology

• 1a: hydro works => viscosity is very low: eta/s=.1-.2 << 1 (Teaney,ES)

• 1b: Because parton cascade requires huge cross sections >> (pQCD 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)

• 1c: charm diffusion: Dc << pQCD predicts (from R_AA and v2 of electrons at RHIC <= Moore+Teaney)

• 1d: very strong jet quenching, including charm, again well beyond pQCD predictions

• 1e: 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• 2a: ``New spectroscopy”: Interaction is strong enough

to make multiple bound states (ES+Zahed, 03), s-wave n=1mesons, colored pairs like qg or non-singlet gg

• 2b: 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)

• 2c: Baryons seem to survive till about 1.6Tc (Liao,ES)• 2d: large energy (up to 4 GeV) 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 barQ - g - g … Q (Liao,ES)

Why do we think that QGP is strongly coupled at RHIC? III: AdS/CFT

N=4 SUSY YM theory at strong coupling at finite T sQGP at RHIC

• 3a: p,e=O( N^2 T^4) even the famous coefficient .8 is better reproduced by the large-g (Klebanov…96) series (3/4+…)

• 3b: viscosity is small: eta/s=1/4pi (Son et al,04)

• 3c:Heavy quark drag and diffusion constant are OK (Yaffe et al, Casalderrey-Teaney) and conical flow is seen (Gubser et al)

• 3d: a complete gravity dual to RHIC collisions => departing black hole/ horizon=>ES,Sin+Zahed, Janik-Peschanski, Gubser…

• 3e: quasiparticles are heavy M*=sqrt(lambda)T>>T and have 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: sQGP is a plasma of fighting electric and magnetic quasiparticles

New (compactified) phase diagramdescribing 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 regionThere 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^16What 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 (‘tHooft, Mandelstam 1980’s) => monopole condensation at T<Tc explains it => 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 E into flux tubes, even in classical plasma!

magnetic flux tubes at the Sun,(work without any superconductor!)

where classical electrons rotate around it

• B: about 1 kG, • Lifetime: few months

A. Nakamura, et al, PRD69(2004)014506

Electric and magnetic screening masses

G. S. Bali, hep-ph/9809351

Dual Superconductor model works well• vacuum with monopole condensate• flux tube as Abrikosov vortex• Seiberg-Witten, a working example

Approaching Tc from above:• E-screening mass decrease less E-charge E-charge getting heavier• M-screening mass increase more M-charge M-charge getting lighter

E/M equilibrium

E dominated

M-dominated

Classical strongly coupled plasmasAs Gamma= <|Epot|>/<Ekin> grows

gas => liquid => solid

Gas, liquid solid

Gelman,ES,Zahed,nucl-th/0601029With a non-Abelian color => Wong eqn

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)

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D∝1/Γ^(0.6 − 0.8)

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!

2^1/)2/2^(/ vvTdtdp −−= λπ

πλπ 4/1/2 =<<= DpTD

Now we compare Dc to weak and strong coupling predictions

The cross is

phenomenological range

added by me, following Moore-Teaney R_AA, v2

Chester and Vuorinen,Hep-ph/0607148

Strong: not veryDiferent from MD

Weak coupling

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1/DT ∝ λ

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D∝1/Γ^(0.6 − 0.8)

==>Range from MDWith differentEQPs/MQPs ratio ==>

Floating matter destributionFriess et al, 0607022

Subsonic emission => no cone(as in b-tagged jets – Antinori,ES, nucl-th/0507046)

subsonic

SupersonicNote how angle moves as v->cs

Short history of developing ``gravity dual” for RHIC

from basically 5dim GR • AdS+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

AdS5 center

(Shu Lin and ES,hep-ph/0610168)

departing 2 heavy ultrarelativistic quarks stretch a longitudinal string

5-dim Pythia model in which strings don’t breakBut fall instead into the 5th dimension

Scaling solution (used inEuclidean appl. By Gross et al,

Makeenko) is only stable ifY<.27 and exist if Y<.5

The non-scaling solutionapproach rectangular shape, small fragmentation regionand rapidity-independent bulk

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τ = t^2 − x^2

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y = (1/2)log[(t − x) /(t = x)]

AdS5 center

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z(τ ,y) = τg(y)

All objects – massless, massive close strings, open strings => fall in AdS 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

New metric, JP at late time(I disagree withJanik on singularity issue)

Old AdS metric

Strething black hole has approximatelyconserved horizon area => entropy

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z(horison)∝ τ ^(1/3)

ConclusionsConclusions StronglyStrongly

coupled QGP coupled QGP has been has been produced at produced at RHICRHIC

robust robust collective collective flows, flows, even even for charm for charm

Strong jet Strong jet quenching quenching

leading to robust leading to robust conical flowconical flow, , now supported by 3-now supported by 3-body correlatorsbody correlators

AdS/CFT => strongly coupled AdS/CFT => strongly coupled conformal regime not too conformal regime not too close to Tcclose to Tc

Heavy quark diffusion and Heavy quark diffusion and quenching in the right ballparkquenching in the right ballpark

conical flow seenconical flow seen hydro explosion can be derived hydro explosion can be derived

from GR =>from GR =>Collapsing membrane, bh formationCollapsing membrane, bh formation

at (1-1.4)Tcat (1-1.4)Tc dominated dominated by magnetic by magnetic QPsQPspostconfinemepostconfinementnt with e-with e-flux flux tubestubes•Classical Classical MD MD is being is being done,done, smaller smaller viscosity due viscosity due to monopoles to monopoles