# Presentation: 471166

## Strongly coupled  QGP:             New Frontiers

*(Quark Matter 2008, *
*Jaipur India)*
*Edward Shuryak*
*Stony Brook*

## 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

## Prologue: multiple views on sQGP (which forced us to learn a lot in the last few years...)

- sQGP

- Plasma
-  physics

- Manybody
-  theory

- Lattice
- simulations

- Gauge theories,
- SUSY models

- Black hole physics,  String theory

**AdS/CFT duality**

**Monopoles**

- Quantum
-  mechanics

- Quasiparticles
- Potentials
- correlators

- Bound states
-  of EQP and MQP
- J/psi,mesons,baryons,calorons

**Stronly coupled**
**cold trapped**
**Atoms: 2nd best liquid**

**Molecular**
**dynamics**

**Transport properties,**
**Entropy generation**

**E/M duality**

- EoS

- Hydrodynamics

- Collective modes
- Energy loss,
- Mach cones

**Flux tubes->**

**Bose-Einstein**
**Condensation**
**->**
**confinement**

- RHIC
- data

## 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, TD****c ****,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? (--)**
**  **

## outline

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

## 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...}

## 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!)

- 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...

- So it may be **even less than **
**Famous ****1/4********!**

- 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**

- D.Molnar talk here

- sQGP is not a
- Gas => Boltsmann
- Approach** inapplicable**
- Yet it can be used
-  with **subdivisions**
- as a model

## 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](http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+%22Li%2C%20Bao%2DAn%22)**__**[ ](http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+%22Li%2C%20Bao%2DAn%22)**__**[Li](http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+%22Li%2C%20Bao%2DAn%22)**_ **nucl-th/9910030      **_**[Heinz](http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+%22Heinz%2C%20Ulrich%20W%2E%22)**_,_[ Kuhlman](http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+%22Kuhlman%2C%20Anthony%22)_  **nucl-th/041105**

## 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**

## Deconfinement and        Electric-magnetic fight/competition in sQGP

- .

**Magnetic quasiparticles** --
**monopoles and dyons --**
**are important/dominant at **
**T< 1.5Tc**
**This affect thermodynamics and**
**especially**** ****transport ****due to**
**nontrivial**** ****“magnetic bottle”**** effect**

## 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**

##  electric/magnetic couplings (e/g) must run in the opposite directions!   

**Old good Dirac condition **
**(in QED-type units e****2****= ********s****)**** **

** ****at the e=g “equilibrium line”**
******s****(el)=**** ********s****(mag)**** ****=1**
**(the best liquid here?)**

**Near deconfinement line  monopoles much lighter than gluons/quarks**
** ****=>********s****(mag)**** small (Landau pole)**
**=> So ********s****(el)**** ****must be strong! **

**n=2 **
**(Higgs A****0****)**

- Liao,ES hep-ph/0611131

******s****(el)********s****(mag)=1**

******s****(el)**

******s****(mag)**

## Electric and magnetic scrreningMasses, Nakamura et al, 2004My arrow shows the ``self-dual” E=M point

**Me>Mm**
**Electrric**
**dominated**

**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/T=O(g)
- ES 78
- MM/T=O(g^2)
- Polyakov 79

**x-Correlations****  **
** ****give MM potential (Mag.length only .1 fm!)**

**monopole density**
**strongly grows **
**as T=> Tc**

**+-**

**++**

## 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

## 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 ](http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+%22Liao%2C%20Jinfeng%22)__[Liao](http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+%22Liao%2C%20Jinfeng%22)_+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

## 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

- 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**

- d

- and interacting weakly

## 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*__* *_

**+**

**-**

**M**

***V***

**E**+

**E**-

- Note that Lorentz force is O(v)!

- Monopole rotates around the electric field line,
-  bouncing off both charges (whatever the sign)

## We found that two charges play ping-pong by a monopole  without even moving! 

**Dual to Budker’s **
** ****magnetic bottle**

- Note that collisions are much
-  more frequent than in cascades

## MD simulation for plasma with monopoles (Liao,ES hep-ph/0611131)   monopole admixture M50=50% etcagain diffusion decreases indefinitely, viscosity does not

- It matters: _50-50 mixture _
- _makes the best liquid, as it_
- _creates __**``maximal trapping”**_

## AdS/CFTdualityfrom 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...)

## 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)

## 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

## 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**

## 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)**

## Maldacena’s dipole  The 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

##  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)

## 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**

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

- W
- O
- R
- L
- D

- A
- N
- T
- I
- 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

**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**

- subsonic

- supersonic

## Photon spectrum has a different shape in sQGP: bremmstrahlung is strongly suppressed while hard photons are enhanced

- sQGP

- wQGP

- Related to talk by Iancu here

## short transport summary log(inverse viscosity s/eta)- vs. log(inverse heavy q diffusion const D*2piT) (avoids messy discussion of couplings)

- RHIC data: very small viscosity and  diffusion
-  **vs theory - AdS/CFT and our MD**

- Weak coupling end =>
- (Perturbative results shown here)
- Both related to mean free path

- MD results, with specified
- monopole fraction

- ->Stronger coupled ->

- Most perfect liquid

- 50-50% E/M is the most ideal liquid

**4pi**

## 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)

## 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.

- 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?**

- 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)**

- T00 , Toi

## 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 **M****m** (for matter)
- => another (more famous) membrane** ****M****h**, (of the “membrane paradigm”) is hovering just above the horizon

## 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

## The story of two membranes III (textbook example)

-  the stretching and falling “matter membrane” **M****m**,    its ends have +/- v
**horizon membrane** **M****h**  bulges upward due to  gravity of Mm till they merge
**Fragmentation regions remain non-thermal** but **in the middle M****m**** gets substituted by M****h,**
-  **observer at midrapidity**
**sees hydrodynamical hologram, but not in fragmentation regions**

- Before equilibration

## 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 r****3****)=const ****(Janik et al)**
**In the ****next to leading order**** (in powers of inverse time)**** there is dissipation induced by the M****h**** viscosity**

## 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****? **

## Conclusions

**Strongly**** ****coupled 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**_

**This makes so “perfect liquid” because of the magnetic-bottle trapping**
** ****the lowest viscosity for 50-50% ****electric/magnetic plasma**

**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

## Thank you, Indian friends!

- Good by,
- Quark Matter 2008,
- Jaipur India

## reserve

## 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**
** **

## 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

## Strong coupling in plasma physics: Gamma= 
/<Ekin> >>1gas => 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)

## RHIC findings: collective flows and jet quenching 
Fundamental questions:
 Why is quark-gluon plasma (sQGP) at RHIC  such a good liquid?
  Is it related to deconfinement?  What is the role of e/m duality 
and magnetic objects in sQGP? 
Do AdS/CFT or e/m dualities explain RHIC results? 
Viscosity and diffusion constant from AdS/CFT, 
  New meaning of dissipation
 Electric and magnetic quasiparticles (EQPs and MQPs) are fighting for dominance  (J.F.Liao,ES, hep-ph/0611131,PRC 07) 
The trapping via 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; both dualities -AdS/CFT and sQGP with monopoles - seem to work. 
Summary:Are they related??? LHC will tell

**Fundamental questions:**
** ****Why is quark-gluon plasma (sQGP) ****at RHIC  ****such a good liquid?**
**  ****Is it related to **_**deconfinement**_**?  What is the role of e/m ****duality **
**and magnetic objects in sQGP? **
**Do AdS/CFT or e/m ****dualities ****explain RHIC results? **
**Viscosity and diffusion constant from**** ****AdS/CFT****, **
**  ****New meaning of dissipation**
** ****Electric and**** ****magnetic**** ****quasiparticles (EQPs and MQPs)**** are fighting for dominance  ****(J.F.Liao,ES, hep-ph/0611131,PRC 07)**** **
**The trapping via 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; both dualities -AdS/CFT and sQGP with monopoles - seem to work. **
**Summary:****Are they related??? LHC will tell**

**Notes:**
Gsi, july 07

## main RHIC finding

- Strong radial and elliptic flows are very well described by ideal hydro => ``the most perfect liquid known”
- 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”

## 2001-2005: hydro describes radial and elliptic flows for all secondaries , pt<2GeV, 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    v_2=<cos(2 phi)>

**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 (RQMD)

- (``strong coupling” ideas before RHIC)

## PHENIX jet pair distribution 

**Note: it is only projection of a cone on phi**
**Note 2: there is also a minimum in**
**<p_t(\phi)> at**
**180 degr., with**
**a value**
**Consistent with background****  **

- The most peripheral bin, here there is no QGP

## An example of ``dyonic baryon”=finite T instantontop.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**