From Einsteinian gravity to strongly coupled QCD via AdS/CFT Edward Shuryak Stony Brook
Download ReportTranscript From Einsteinian gravity to strongly coupled QCD via AdS/CFT Edward Shuryak Stony Brook
From Einsteinian gravity to strongly coupled QCD via AdS/CFT
(Einstein Coll.
Rehovot, Dec.2007) Edward Shuryak Stony Brook
Einstein
We should be happy to see a bit of Einstein in each other , even if it measures in milligramms!
Why this picture? He seems to be less professorial and happier than in most other photos The beach looks like Stony Brook (?) where he indeed rented for few summers. He was at those beaches when was asked to write the famous letter to Roosevelt
Outline
The puzzle: RHIC findings -- collective flows and jet quenching -- QGP is very strongly coupled! What exactly it means?
AdS/CFT intro. Understanding analogs for Coulomb/Ampere.. Laws at strong coupling Viscosity and diffusion constant from AdS/CFT Calculating the “hologramm” for a dipole, conical flow, a falling string => gravity dual for high energy collisions
Creation of black holes: new meaning of dissipation transport summary; two explanations -AdS/CFT and sQGP with monopoles - seem to work. Summary:
The main puzzle: Quark-Gluon Plasma is unusual matter
• RHIC experiments (2000-now) AuAu at 200 GeV/N • QGP fireball of few10 3 particles behaves hydrodynamically • Viscosity 10 times lower than of anything else: the best known liquid!
• Jets lose energy very strongly --drag force is order of magnitude larger than expected from kinetic estimates, •
Same for heavy quarks
• Energy is not going into forward cone of radiation, as expected perturbatively, but to a ``conical flow”
• • •
Sonic boom from quenched jets
Casalderrey,ES,Teaney, hep ph/0410067; H.Stocker…
Wake effect or “sonic boom”
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
Two hydro modes can be excited
(from our linearized hydro solution):
a ``diffuson” a sound
PHENIX jet pair distribution
Note: it is only projection of a cone on phi Note 2: there is also a minimum in
The most peripheral bin, here there is no QGP
AdS/CFT from gravity in AdS
5
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 information falls into black hole: only total entropy=area of newly formed b.h.horizon = remains …
The first gauge-string duality found in 1997
AdS/CFT correpondence known as ``Maldacena duality” Along the long path illuminated by Witten,Polyakov,Klebanov…
The duality setting
• CFT (conformal gauge theory) N=4 SYM a cousin of QCD (chromodynamics=theory of strong interaction) in which the coupling AdS (anti-de-Sitter)
=g 2 N c does not run.
• It lives on the 4-dim boundary of 5-d curved space where (super) gravity is a description of (super) string theory • Correspondence dictionary: everything in the “bulk” reflects 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 complect plane and get math to simplify the problem.
What “strongly coupled” means
• QED e 2 /hbar c=1/137
<<1
• Atoms and positronium are weakly bound E=m e (1 rel.corr
• What happens as grows? Klein-Gordon (Dirac) eqns predict particles
fall at each other
(1s state falls at and then other levels as it grows • Strong coupling is large g 2 N c = N c >>1 yet AdS/CFT told us
charges do not fall
1s state has energy O(M/ sqrt( and
The 5th coordinate
• z is the 5th coordinate, dim=length=1/momentum • its physical meaning is ``scale” as in renorm.group
• z=>0 is ``high scale” UV or very high energies, z=>infinity is low scale or IR • ds 2 =(-dt 2 +dx 1 2 +dx 2 2 +dx 3 2 +dz 2 )/z 2 so distances in z are logarithmic. Light speed is still 1 in all directions • Gravity force is acting toward large z, so “stones” fall there
The story of Maldacena’s dipole
(example of how little we understand N=4 SYM) • Maldacena,Rey,Yee -98 one of the first apps: • The pending string (=flux tube) has minimal action • Modified Coulomb law at strong coupling, sqrt of the coupling << coupling • Can it be just a factor, like dielectric constant?
z
Can one get it resumming diagrams?
• ‘tHooft said large Nc leads to
planar
diagrams, but nobody knows how to do it • Semenoff and Zarembo hep-th/0202156 summed
ladder
diagrams, The lesson: ES,Zahed hep-th/0308073 Parametrically short time of color correlation, or effective Velocity >>1
More on the dipole in a stronly coupled vacuum • Shu Lin,ES arXiv:0707.3135 recently evaluated holographic stress tensor from the Maldacena string • T 00 ->d 3 /r 7 Times function of the Angle which is plotted On the right
•
• Previously Callan&Guijosa calculated a scalar ”dilaton image” • (F
2
=d
3
/r
7
and no angular function • Why extra d/r?
Klebanov,Maldacena,Thorn
hep-th/0602255 : for the same reason as 1/sqrt(
short time of color correlations! Fields of both charges can only cancel each other if emitted nearsimulaneously Thus it is not just a dielectric constant, r and angular depenedence are also changed!
One can also do charge+monopole
• J.Minahan 98 E=- f(g 2 /4 ) sqrt(N)/L with self-dual f(g 2 /4 ) = f( 1/(g 2 /4 ) • We calculated stress tensor from this configuration • In weakly coupled gauge theory Poynting T 0i rotates around the line of two charges (J.J.Thomson) but we found it to be zero at strongly coupled CFT!
viscosity from AdS/CFT
• • (Polykastro,Son, Starinets 03) Kubo formula
s
hbar
Left vertical line is our 4d Universe, (x,y are on it) /4 Temperature is given by position of a horizon (vertical line, separationg • • From interier of``black brane” 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 One quark A (fisherman) is N In our world, T The other (fish) in I Antiworld W (=conj.amplitude) String connects them and conduct waves in one direction through the black hole O R L D W O R L D
Heavy quark in CFT plasma
has a string deformed by ``hot wind” Herzog,Yaffe,Gubser… May06 calculated the drag force = momentum Flow down the string
Einstein relation between Drag and diffusion is Fulfilled: But how graviy knows?
subsonic supersonic
from P.Chesler,L.Yaffe
(also Gubser et al have detailed papers On this) Both groups made amazingly detailed Description of the conical flow from AdS/CFT=> Note that it is not hydro but direct soluiton: one can e.g.
Be sure the shape of the wave is correct Even at micro scales
Gravity dual to the (heavy quark) collision: “Lund model” in AdS/CFT (Lin,ES hep-ph/0610168 ) If colliding objects made of heavy quarks • • Stretching strings -- are falling under the AdS gravity and don’t break analytic solution at v non hydrodynamical explosion observed in our 4d world AdS 5 Center= Extremal b.h. • • Holographic image of a falling string (as far as we know the first time dependent hologramm) • • T 00 , T oi Cannot be reprensented as hydrodynamical => anisotropic pressure in the ``comoving frame” • AdS metric corresponds to extreme BH (mass is minimal for its charge and no horizon) • As collision creates falling “debris”, they will form a non-extreme BH with a horizon Nastase 03 • This can only be done via non-linearized Einstein eqns • Expanding/cooling fireball= departing horizon (Sin,ES and Zahed 04, …) • Asimptotic late-time solution in 1+1 dim is found , stretching BH (Janik-Peschanski 05) • Relaxation=formation of a horizon (trapping surface) where information is lost (is it true for dynamically stretched t-dependent horizon? Yes to PJ leading order only) returns pure thermal Hawking radiation => with hydrodynamical hologramm • W.Israel => collapsing shell gets heated, explains the origin of entropy production Fraction of quasiparticles are magnetically Charged (monopoles and dyons) At T 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 Electric and magnetic scrrening Masses , Nakamura et al, 2004 My arrow shows the ``self-dual ” E=M point Me M E /T=O(g) ES 78 M M /T=O(g^2) Polyakov 79 New (compactified) phase diagram describing 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 all blue region, not only in the confined phase! In fact, they are maximally enhanced at Tc • • Strong coupling in plasma physics: Gamma= <|Epot|>/ 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 Gelman,ES, Zahed,nucl th/0601029 With a non-Abelian color => Wong eqn Gas, liquid solid static eDipole+MPS 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) We found that two charges play 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% etc again diffusion decreases indefinitely, viscosity does not D 1/ ^( 0.6 0.8) It matters: 50-50 mixture makes the best liquid, as it creates ``maximal trapping” • • log(inverse viscosity s/eta )- vs. log(inverse heavy q diffusion const D*2piT ) (avoids messy discussion of couplings) ->Stronger coupled -> Most perfect liquid RHIC data: very small viscosity and D vs theory - AdS/CFT and MD (soon to be explained) 4pi 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 (I don’t mean the price of LHC but ALICE) 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…) 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 Good liquid because of magnetic bottle trapping Classical MD is being done, the lowest viscosity for 50-50% electric/magneti c plasma AdS/CFT => natural applications of string theory, N=4 SYM is not QCD: nonconfining and Strongly coupled, sQGP is OK RHIC data on transport (eta,D), ADS/CFT and classical MD all qualitatively agree! Are these two pictures related? s (not <0.3 as in pQCD applications) tHooft lambda=g 2 Nc=4piNc=O(20)>>1-1 Bielefeld-BNL lattice group: Karsch et al 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/N naighbours ) We calculated ``instantons” for particles jumping paths in a liquid and solid He4 incuding realistic atomic potentials and understood 2 known effects: (i) Why Tc grows with repulsive interaction<= because a jump proceeds faster under the barrier (ii) no supersolid He => density too large and action when above critical Marco is doing Path Integral simulations with permutations numerically, to refine conditions BEC transitions take place Jumping paths: Feynman, interacting 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) For charged Bose gas (monopoles) the action for the jump can be calculated similarly, but relativistically; jumps in space d and in time Comparable) ∆S=M sqrt(d 2 +(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 MeVGravity dual for the heavy ion collisions
New meaning of dissipation •
• Its area gives the entropy:
• It
Another duality for sQGP: electric/magnetic fight
So why is such plasma a good liquid? Because of magnetic-bottle trapping:
short transport summary
From RHIC to LHC: (no answers, only 1bn$ questions)
Conclusions
reserve
Effective coupling is large! alpha
=O(1/2-1)
Bose condensation versus repulsive scattering length
BEC (confinement) condition for monopoles