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Understanding strongly coupled quark-gluon plasma (sQGP). (SIS program, Cambridge, Aug.2007) Edward Shuryak Stony Brook. The emerging theory of sQGP. Quantum mechanics. Stronly coupled cold trapped atoms. Manybody theory. Lattice simulations. sQGP. Quasiparticles Potentials

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understanding strongly coupled quark gluon plasma sqgp

Understanding strongly coupled quark-gluon plasma (sQGP)

(SIS program,

Cambridge, Aug.2007)

Edward Shuryak

Stony Brook

the emerging theory of sqgp
The emerging theory of sQGP



Stronly coupled

cold trapped










Bound states

of EQP and MQP







Flux tubes->







Transport properties



E/M duality

Energy loss,

Collective modes

Mach cones


Gauge theories,

SUSY models

String theory


Qs: Why do we have strongly coupled quark-gluon plasma (sQGP) at RHIC? Is it related to deconfinement (T=(1-1.5)Tc) or quasi-conformal behaviour at $T>1.5Tc? What is the role of magnetic objects? Can one explain RHIC results using AdS/CFT? A picture is emerging…

  • RHIC findings: collective flows and jet quenching
  • Viscosity and diffusion constant from AdS/CFT, complete gravity dual?
  • Phase diagram and lattice. Electric andmagneticquasiparticles (EQPs and MQPs) are fighting for dominance (J.F.Liao,ES, hep-ph/0611131,PRC 07)Flux tube existence/dissolution (J.F.Liao,ES, 0706.4465[hep-ph]) the magnetic bottle effect
  • molecular dynamics (MD) of Non-Abelian plasma with monopoles(B.Gelman, I.Zahed,ES, PRC74,044908,044909 (2006), J.F.Liao,ES, hep-ph/0611131,PRC 07):
  • transport summary; From RHIC to LHC
  • Summary: are two explanations related???
rhic findings
RHIC findings
  • Strong radial and elliptic flows are very well described by ideal hydro => ``perfect liquid”
  • Strong jet quenching, well beyond pQCD gluon radiation rate, same for heavy charm quarks (b coming)
  • Jets destroyed and their energy goes into hydrodynamical ``conical flow”
from magdeburg hemispheres 1656 to dreams of 1970 s
From Magdeburg hemispheres (1656) to dreams of 1970’s…

QCD vacuum is

so compicated…

    • “We cannot pump out complicated objects populating the QCD vacuum, but we can pump in something else, namely the Quark-Gluon Plasma, and measure explosion”
  • (QGP in 1970’s was expected to be just a simple near-ideal quark-gluon gas, to ``fill the bag”)
one may have an absolutely correct theory and still make accidental discoveries
One may have an absolutely correct theory and stillmake 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, sQGP

how hydrodynamics works at rhic
How Hydrodynamics Works at RHIC

Elliptic flow

How does the system respond to initial spatial anisotropy?

Dense or dilute?

If dense, thermalization?

If thermalized, EoS?



The coolest thing on Earth, T=10 nK or 10^(-12) eV can actually produce a Micro-Bang ! (O’Hara et al, Duke )

Elliptic flow with ultracold trapped Li6 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

Similar mechanism was proposed (Zahed and myself) for QGP, in which a pair of quasiparticles is in resonance with their bound state at the “zero binding lines”




2001-2005: hydro describes radial and elliptic flows for all secondaries , pt<2GeV, centralities, rapidities, A (Cu,Au)… Experimentalists were very sceptical but wereconvinced and ``near-perfect liquid” is now official, =>AIP declared this to be discovery #1 of 2005 in physicsv_2=<cos(2 phi)>



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 (RQMD)

one more surprise from rhic strong jet quenching and flow of heavy quarks
One more surprise from RHIC: strong jet quenching and flow of heavy quarks


Heavy quark quenching as strong as for light gluon-q jets!

Radiative energy loss only fails to reproduce v2HF.

Heavy quark elliptic flow: v2HF(pt<2GeV) is about the same as for all hadrons!


Small relaxation time t or diffusion coefficient DHQinferred for charm.

sonic boom from quenched jets casalderrey es teaney hep ph 0410067 h stocker

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
phenix jet pair distribution
PHENIX jet pair distribution

Note: it is only projection of a cone on phi

Note 2: more

recent data from

STAR find also a minimum in

<p_t(\phi)> at

180 degr., with

a value

Consistent with background

The most peripheral bin, here no matter

ads cft from gravity in ads 5 to strongly coupled cft n 4 sym plasma
AdS/CFTfrom gravity in AdS5 to strongly coupled CFT (N=4 SYM) plasma

what people dream about for LHC

experments -- a black hole formation --

does happen, in each and every RHIC AuAu event =>

thermalization, All info is lost except the overall entropy=area of newly formed b.h.horizon

viscosity from ads cft polykastro son starinets 03 kubo formula t ij x t ij y
viscosity from AdS/CFT(Polykastro,Son, Starinets 03)Kubo formula <Tij(x)Tij(y)>=>
  • Left vertical line is our 4d Universe, (x,y are on it)
  • Temperature is given by position of a horizon (vertical line, separationg
  • From interier of``black brane” T=T(Howking radiation) (Witten 98)
  • Correlator needed is just a graviton propagator G(x,y)
  • 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

heavy quark diffusion j casalderrey d teaney hep ph 0605199 hep th 0701123
Heavy quark diffusion J.Casalderrey+ D.Teaney,hep-ph/0605199,hep-th/0701123






One quark (fisherman) is

In our world,

The other (fish) in



String connects them and conduct waves in one direction through the black hole













Left: P.Chesler,L.Yaffe

Up- from Gubser et al

Both groups made

Amasingly detailed

Description of the

conical flow from

AdS/CFT=> not much

is diffused

gravity dual to the whole collision lund model in ads cft
Gravity dual to the whole collision: “Lund model” in AdS/CFT
  • Expanding/cooling fireball= departing Black Hole

(Nastase 03, Sin,ES and Zahed 04,Janik-Peschanski 05…)

If colliding objects made of heavy quarks

  • Stretching strings -- unlike Lund model those are falling under the AdS gravity and don’t break (Lin,ES hep-ph/0610168)
  • The falling membrane is created which separate two regions of two different metrics: it is becoming a b.h. horizon

Now linearized version in progress

(field from a static Maldacena string recently done Lin,ES arXiv:0707.3135, T00 ->1/r7 )



Extremal b.h.

ads cft suggests completely new pictures of gauge theory topology
AdS/CFT suggests completely new pictures of gauge theory topology
  • Instantons = D-1 brane=point in the bulk, at large Nc coalesce together(Mattis,Khose,Dorey 90’s)
  • Monopoles = endpoints of D1 (string-like) branes
  • Electric-magnetic duality includes duality between baryons and calorons (finite T instantons) as Nc monopoles (known before ads <= Kraan,van Baal ….)
explaining transport in sqgp electric magnetic fight classical qgp and its molecular dynamics
Explaining transport in sQGP:electric/magnetic fight“Classical QGP” and its Molecular Dynamics

Electrons have the same charge -e all the time,

but our quasiparticles (quarks, gluons,…) have colors

which is changing in time

Fraction of quasiparticles are magnetically

Charged (monopoles and dyons) which

fight each other

At T<Tc they somehow (?) make a

“dual superconductor”


An example of ``dyonic baryon”=finite T instantontop.charge Q=1 config.,dyons identified via fermionic zero modes

Berlin group - Ilgenfritz et al

Red,blue and green U(1) fields

3 dyons with corresp.

Field strengths, SU(3),

Each (1,-1,0) charges

electric and magnetic scrrening masses nakamura et al 2004 my arrow shows the self dual e m point
Electric and magnetic scrreningMasses, Nakamura et al, 2004My arrow shows the ``self-dual” E=M point




At T=0 magnetic

Screening mass

Is about 2 GeV

(de Forcrand et al)

(a glueball mass)

Other data (Karsch et al) better show how Me

Vanishes at Tc





ES 78


Polyakov 79

new compactified phase diagram describing an electric vs magnetic competition
New (compactified) phase diagramdescribing an electric-vs-magnetic competition

Dirac condition (old QED-type units e^2=alpha, deliberately no Nc yet)

<- n=2 adjoint

Thus at the e=g line

Near deconfinement line g->0 in IR

(Landau’s U(1) asymptotic freedom)

=> e-strong-coupling because g in weak!

Why is this diagram better? =>

There are e-flux tubes in allblue region, not only in the confined phase! In fact, they are maximally enhanced at Tc

Energy and entropy associated with 2 static quarksis very large near Tcfrom lattice potntials Bielefeld-BNL

pQCD predicts

a negative U

  • R->infinity means there are 2 separate objects
  • Entropy=20 implies exp(20) states
  • At R=(.3-1.2)fm both are about linear in R <=

What object is that?

Energy and entropy associated with 2 static quarksis very large near Tcfrom lattice potntials Bielefeld-BNL

pQCD predicts

a negative U

  • R->infinity means there are 2 separate objects
  • Entropy=20 implies exp(20) states
  • At R=(.3-1.2)fm both are about linear in R <=

What object is that?

e flux tubes above tc with j f liao archive 0706 4465 hep ph
e-flux tubes above Tc?(with J.F.Liao, archive 0706.4465 [hep-ph])
  • Dual superconductivityat T<Tcas a confinement mechanism (‘tHooft, Mandelstam 1980’s) => monopole Bose condensation => electric flux tubes (dual to Abrikosov-Nielsson-Olesen vortices)
  • Can uncondenced MQPs do the same at T>Tc ?MQPs are reflected from a region with E field => pressure => flux tubes compression in plasma
  • We solve quantum mechanics of motion in each partial wave
magnetic flux tubes at the Sun,(work without any superconductor!): so we need to work out the exact conditions

where classical electrons rotate around it

  • B: about 1 kG,
  • Lifetime: few months
classical and quantum mechanics of the flux tube
Classical and quantum mechanics of the flux tube

Red trajectory A => nu=0

(velocity at large r directed to the center)

Black one B => m=0 (which goes through

the center because no m^2/r^2 barrier)

dissolution of the tube roughly at t 1 4tc lattice bielefeld bnl
dissolution of the tube roughly at T>1.4Tc(lattice Bielefeld-BNL)
  • Assuming this is the case and using our criterion we get density of magnetic QPs=>
  • n(magnetic,T=1.3Tc)=(4-6)fm-3
  • Twice less than about 10 fm^-3 at T=0 (Bali et al, from vacuum confining strings)
is sqgp full of flux tubes evolution with t
Is sQGP full of flux tubes? evolution with T:
  • T=0, dual Meissner =>ANO
  • At T<Tc complicated shape can produce entropy=o(L) but it is Nc independent => no electric objects, no color changed
  • At T>Tc heavy gluon (and quark) quasiparticles first appear as ``beads”S=(L/a)log7+(L/b)log(Nc)
  • As T grows further => less monopoles of higher energy => no electric field flux suppression =>``electric polymers”
  • Very high T => wQGP, electric plasma, no bound states

(Presumably gluons-in-the-tube correspond to AdS/CFT

Minahan string solutions and are also dual

to monopoles-in-the-tube solutions recently

Worked out by Tong et al,Shifman et al)

bose einstein condensation of interacting particles monopoles with m cristoforetti trento
Bose-Einstein condensation of interacting particles(=monopoles)(with M.Cristoforetti,Trento)
  • Feynman theory (for liquid He4): polygon jumps BEC if exp(-∆S(jump))>.16 or so (1/Nnaighbours)

We calculated ``instantons” for particles jumping paths in a liquid and

solid He4 incuding realistic atomic potentials and understood 2 known effects:

Why Tc grows with repulsive interaction<= because a jump proceeds faster under the barrier

(ii) no supersolid He => density too large and action above critical

Marco is doing Path Integral simulations with permutations numerically, to refine conditions when BEC transitions take place





bec confinement condition for monopoles
BEC (confinement) condition for monopoles

For charged Bose gas (monopoles) the action for the jump can be calculated similarly, but relativistically; jumps in space d and in time


∆S=M sqrt(d2+(1/Tc)2)+ ∆S(interaction) = Sc =1.65-1.89

(first value from Einstein ideal gas, second from liquid He)

provides the monopole mass M at Tc

M Tc approx 1.5 =>

M as low as 300 MeV

strong coupling in plasma physics gamma epot ekin 1 gas liquid solid
Strong coupling in plasma physics: Gamma= <|Epot|>/<Ekin> >>1gas => liquid => solid
  • This is of course for +/- Abelian charges,
  • But ``green” and ``anti-green” 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 sQGP)

Wong eqn can be rewritten as x-p canonical pairs,

1 pair for SU(2), 3 for SU(3), etc. known as

Darboux variables. We did SU(2) color => Q is a unit

vector on O(3)



With a non-Abelian color => Wong eqn

Gas, liquid solid

so why is such plasma a good liquid because of magnetic bottle trapping static edipole mps
So why is such plasma a good liquid? Because of magnetic-bottle trapping: static eDipole+MPS

Note that Lorentz force is O(v)!







we found that two charges play ping pong by a monopole without even moving
We found that two chargesplay ping-pong 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 M50=50% etcagain diffusion decreases indefinitely, viscosity does not

It matters: 50-50 mixture

makes the best liquid, as it

creates ``maximal confusion”


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 D
  • vs theory - AdS/CFT and MD(soon to be explained)

Most perfect liquid


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

from rhic to lhc no answers only 1bn questions
From RHIC to LHC:(no answers, only 1bn$ questions)
  • Will ``perfect liquid” be still there?
  • Is jet quenching as strong, especially for c,b quark jets and much larger pt?
  • Is matter response (conical flow at Mach angle) similar? (This is most sensitive to viscosity…)
from sps to lhc
From SPS to LHC
  • lifetime of QGP phase nearly doubles, but v2 grows only a little, to a universal value corresponding to EoS 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 S.Bass)

Strongly coupled QGP is produced at RHIC T=(1-2)Tc

This is the region where transition from magnetic to electric dominance happen

at T<1.4 Tc still Lots of magnetic objects =>

E-flux tubes

RHIC data on transport (eta,D), ADS/CFT and classical MD all qualitatively agree !

Are these two pictures related?

  • Good liquid because of magnetic-bottle trapping
  • Classical MD is being done, lowest viscosity for 50-50% electric/magnetic plasma
  • AdS/CFT => natural applications of string theory
  • N=4 SYM is nonconfining and
  • Strongly coupled!
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

At e=m line both effective gluons and monopoles have masses M about 3T exp(-3)<<1 is our classical parameter

(Boltzmann statistics is good enough)

  • At T=Tc monopoles presumably go into Bose-Einsetein condensation => new semiclassical theory of it for strongly interacting Bose gases, tested on He4
  • (M.Cristoforetti, ES, in progress)