Strongly coupled QGP: New Frontiers

1
Strongly coupled QGP New Frontiers

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

2
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 gt the critical and the softest
  points

3
Prologue multiple views on sQGP (which forced us
to learn a lot in the last few years)
Quantum mechanics
Stronly coupled cold trapped Atoms 2nd best
liquid
Manybody theory
Lattice simulations
Quasiparticles Potentials correlators
Bound states of EQP and MQP J/psi,mesons,baryons,
calorons
Bose-Einstein Condensation -gt confinement
EoS
Flux tubes-gt

• sQGP

RHIC data
Hydrodynamics
Molecular dynamics
Monopoles
Transport properties, Entropy generation
Plasma physics
E/M duality
Collective modes Energy loss, Mach cones
AdS/CFT duality
Gauge theories, SUSY models
Black hole physics, String theory
4
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, TDc ,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? (--)

5
outline

• A bit of hydro
• Electric-magnetic duality (fight,competition)
• Gauge-string duality - AdS/CFT
• Out of equilibium sGlasmagtsQGP
• conclusions

6
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 ltngtabout s1/4
• Pomeranchuck (1952) introduced freezeout
• Landau (1953) explained that one should use hydro
  in between, saving Fermis prediction via entropy
  conservation he also suggested it should work
  because coupling runs to strong at small
  distance! No asymptotic freedom yet in 1950s

7
My own hydro history

• Hydro for ee- as a spherical explosion PLB
  34 (1971) 509
• gt killed in 1973 by as.freedom and in 1976 by
  SLAC discovery of jets in ee-
• Looking for it in pp transverse flow at ISR,
  ESZhirov, PLB (1979) 253
• gtKilled by apparent absence of transverse
  flow in pp
• ESHung, prc57 (1998) 1891, radial flow at PbPb
  at CERN SPS worked (but only with correct
  differential freezeout surfaces!)

8

• main RHIC finding Strong radial and elliptic
  flows are very well described by ideal hydro
  2001-2002 hydro describes radial and elliptic
  flows for all secondaries , ptlt2GeV,
  centralities, rapidities, A (Cu,Au) Most
  theorists/experimentalists were very sceptical
  but were eventially convinced and the term picked
  up by D.Teaney and myself in 2003 gt the
  most perfect liquid known gets officialgtAIP
  declared this to be discovery 1 of 2005 in
  physics
• Jets destroyed and their energy goes into
  hydrodynamical conical flow
  H.Stocker 04, Casalderrey,ES,Teaney 04.

Btw, Mach cone ideas of 1970s did not work
because nucleai Are not such perfect liquid as
sQGP
9
So it may be even less than Famous 1/4?!
10

• Corrections are small for such eta/s
• Especially at final/later time
• v2(pt) is changing at the tail and improves
• Agreement at ptgt1 GeV
• But (my comment) relying on small tails
• is dangerous

11
D.Molnar talk here
sQGP is not a Gas gt Boltsmann Approach
inapplicable Yet it can be used with
subdivisions as a model
12
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 Li nucl-th/9910030
  Heinz, Kuhlman nucl-th/041105

13
4??/slt1? Generalized viscosity from AdS/CFT
(sound) decreases with k/T, (although we dont
know why)

• M.LublinskyES, 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

14
Deconfinement and Electric-magnetic
fight/competition in sQGP
.
Magnetic quasiparticles -- monopoles and dyons
-- are important/dominant at Tlt 1.5Tc This
affect thermodynamics and especially transport
due to nontrivial magnetic bottle effect
15
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 N2
  SYM

16
electric/magnetic couplings (e/g) must run in
the opposite directions!
Liao,ES hep-ph/0611131
Old good Dirac condition (in QED-type units e2
?s)
n2 (Higgs A0)
?s(el)?s(mag)1
?s(el)
at the eg equilibrium line ?s(el) ?s(mag)
1 (the best liquid here?)
?s(mag)
Near deconfinement line monopoles much lighter
than gluons/quarks gt?s(mag) small (Landau
pole) gt So ?s(el) must be strong!
17
Electric and magnetic scrreningMasses, Nakamura
et al, 2004My arrow shows the self-dual EM
point
MeltMm Magnetic Dominated At T0
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)
MegtMm Electrric dominated
ME/TO(g) ES 78 MM/TO(g2) Polyakov 79
18
x-Correlations give MM potential (Mag.length
only .1 fm!)
-
monopole density strongly grows as Tgt Tc

19
Very recent data (thanks to M.DElia)confirm
that correlation strength increases with T,
indeed opposite to electric
So at least the magnetic coupling does behave as
Landau thought
20
Understanding monopole dynamics

• Claudia RattiES HiggsingltL(T)gt for g,q,
• tHooft-Polyakov monopoles lattice data (e.g
  n(mon,T)) gtmasses of q,g,m and
  ?s(el,T),?s(mag,T)
• Electric Flux Tubes in Magnetic Plasma.?Jinfeng
  LiaoES arXiv0706.4465 derives conditions for
  (meta) stable flux tubes at TgtTc and explains
  lattice data on static potentials
• Marco Cristoforetti ES Bose-condensation in
  strongly interacting liquids gt Monopole mass at
  Tc from Feynman condition

21
Bose-Einstein condensation of strongly
interacting particles (with M.Cristoforetti,now
TU Munich)

• Feynman theory polygon jumps BEC if
  ?S(jump)ltSc1.65-1.8

d

• 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
• ?SM sqrt(d2(1/Tc)2) Sc
• gt M(mon, T Tc)O(300 MeV) ltlt M(g,q)O(800
  MeV)

Jumping paths Feynman, interacting
and interacting weakly
22
So why is such plasma a good liquid? Because of
magnetic-bottle trapping static eDipoleMPS
Note that Lorentz force is O(v)!

E
M
V
E-
-
Monopole rotates around the electric field line,
bouncing off both charges (whatever the sign)
23
We found that two charges play ping-pong by a
monopole without even moving!
Note that collisions are much more frequent than
in cascades

• Dual to Budkers
• magnetic bottle

24
MD simulation for plasma with monopoles (Liao,ES
hep-ph/0611131) monopole admixture M5050
etcagain diffusion decreases indefinitely,
viscosity does not
It matters 50-50 mixture makes the best liquid,
as it creates maximal trapping
25
AdS/CFTdualityfrom gravity in AdS5 to strongly
coupled CFT (N4 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)

26
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)

27
How can it help us?

• T0 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

28
The duality setting

• CFT (conformal gauge theory) N4 SYM a cousin of
  QCD (chromodynamicstheory 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

29
The 5th coordinate

• the 5th coordinate z, dimlength1/momentum
• its physical meaning is a scale as in
  renorm.group
• zgt0 is high scale UV or very high energies,
  zgtinfinity is low scale or IR
• ds2 (-dt2dx12 dx22 dx32 dz2)/z2 so
  distances in z are logarithmic.
  Light speed is still 1 in all directions
• zL2/r where r is distance from b.h. gt
• 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)

30
Maldacenas 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 ltlt (g2N)
  because of short-time color correlations
  ESZahed,04
• Can it be just a factor, like a dielectric
  constant?

z
31
A hologramm of a dipole in a stronly coupled
vacuum not just dielectric constant and not even
only electric E!

• Shu Lin,ES arXiv0707.3135
• recently evaluated holographic
• stress tensor from the
• Maldacena string
• Here is large r behavior
• T00 gt(g2N)1/2d3/r7
• Times function of the
• Angle which is plotted by a solid line
• (to be compared to zero coupling
• gt(g2N)d2/r6
• Times another function (dashed)

32
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 ltTij(x)Tij(y)gt gt 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 propertiesT.Damour
  (1982) gt 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)
• gt dissipation is at the bottom since horizon
  membrane is black

33
Heavy quark diffusion J.Casalderrey
D.Teaney,hep-ph/0605199,hep-th/0701123
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
A N T I W O R L D
34
subsonic
supersonic
Left P.Chesler,L.Yaffe Up- from Gubser et
al Both groups made Amasingly
detailed Description of the conical flow from
AdS/CFTgtvery close to hydro but corrections can
be inferred
35
Photon spectrum has a different shape in sQGP
bremmstrahlung is strongly suppressed while hard
photons are enhanced
Related to talk by Iancu here
wQGP
sQGP
36
short transport summary log(inverse viscosity
s/eta)- vs. log(inverse heavy q diffusion const
D2piT) (avoids messy discussion of couplings)
-gtStronger coupled -gt
Most perfect liquid

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

4pi
MD results, with specified monopole fraction
Weak coupling end gt (Perturbative results shown
here) Both related to mean free path
50-50 E/M is the most ideal liquid
37
Non-equilibrium gravity dual gt sGLASMA

• From cold T0 (extreme BH mass is minimal for
  its charge gt no horizon AdS ) to hot non-extreme
  BH with a horizon gt T
• extra mass from collision created falling
  strings Advantages naturally dissipativeclassic
  alproduce correct Bekenstein entropy S
• Expanding/cooling fireball departing b.h.
  horizon in different geometries 1d, d1,2,3
  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 Bang13
  departing BH, (Sin,ES and Zahed 04, in ADS
  Horowitz,Itzhaki,99, Gubser et al, 06)
• non-dissipative explosion in 11 dim (Kajantie
  et al 07)

38
Gravity dual to the (ee-gtheavy quarks)
collision Lund model in AdS/CFT (Shu Lin,ES,
III papers )

• If colliding objects are made of heavy quarks
• Stretching strings are falling under the AdS
  gravity and dont break
• Instability of simple scaling solution and
  numerical studies
• Analogs of longitudinal E,B in wGLASMA

AdS5 center Extremal b.h.
39

• a holographic image of this process,
• lt time-dependent Green function for linearized
  Einstein eqns
• How does it look for a falling string?
• Is it hydro-like explosion or not?

40
T00 , Toi

• 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! gt anisotropic pressure in the comoving
  frame
• (like in Rajus wGLASMA)

41
The story of two membranes(Many strings falling
together)

• Imagine 2 walls of heavy quarks gt 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 Mm (for matter)
  
• gt another (more famous) membrane Mh, (of the
  membrane paradigm) is hovering just above the
  horizon

42
The story of two membranes II (textbook example)
Curvature at membrane jumps gt Israel
junction condition

• 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

43
The story of two membranes III (textbook example)
Before equilibration

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

44
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 xvt, it moves in
  zO(t1/3)1/r so A4S O(x r3)const (Janik et
  al)
• In the next to leading order (in powers of
  inverse time) there is dissipation induced by the
  Mh viscosity

45
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?

46
Conclusions

• AdS/CFT gt 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

• Strongly coupled QGP produced at RHIC is at
  T(1-2)Tc gt
• This is the region where electric/magnetic
  couplings cross

• Non-equilibrium time-dependent
• AdS/CFT sGLASMA
• Two-membranes paradigm gthorizon provides T
• Equilibration/entropy production in sQGP can
  benefit from 30 years or work on gravitational
  collapse30 years of string theory

• This makes so perfect liquid because of the
  magnetic-bottle trapping
• the lowest viscosity for 50-50
  electric/magnetic plasma

47
Thank you, Indian friends!

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

48
reserve
49
Sonic boom from quenched jets Casalderrey,ES,Teane
y, 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

50
Effective coupling is large! alphasO(1/2-1) (not
lt0.3 as in pQCD applications)tHooft
lambdag2Nc4piNcO(20)gtgt1-1
Bielefeld-BNL lattice group Karsch et al
51
Strong coupling in plasma physics Gamma
ltEpotgt/ltEkingt gtgt1gas gt liquid gt 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
• ltpotgt/ltkingtO(60), about 3-10 in sQGP)

52

• 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.
• SummaryAre they related??? LHC will tell

53
main RHIC finding

• Strong radial and elliptic flows are very well
  described by ideal hydro gt 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

54
2001-2005 hydro describes radial and elliptic
flows for all secondaries , ptlt2GeV,
centralities, rapidities, A (Cu,Au)
Experimentalists were very sceptical but
wereconvinced and near-perfect liquid is now
official, gtAIP declared this to be discovery 1
of 2005 in physics v_2ltcos(2 phi)gt
(strong coupling ideas before RHIC)
PHENIX, Nucl-ex/0410003 red lines are for
ESLauretTeaney 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)
55
PHENIX jet pair distribution
Note it is only projection of a cone on
phi Note 2 there is also a minimum
in ltp_t(\phi)gt at 180 degr., with a
value Consistent with background
The most peripheral bin, here there is no QGP
56
An example of dyonic baryonfinite T
instantontop.charge Q1 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