From Einsteinian gravity to strongly coupled QCD via AdS/CFT

From Einsteinian gravity to strongly coupled QCD via AdS/CFT

(Einstein Coll.(Einstein Coll.Rehovot, Dec.2007)Rehovot, Dec.2007)

Edward ShuryakEdward ShuryakStony BrookStony Brook

(Einstein Coll.(Einstein Coll.Rehovot, Dec.2007)Rehovot, Dec.2007)

Edward ShuryakEdward ShuryakStony BrookStony Brook

EinsteinEinstein We should be happy to see a We should be happy to see a

bit of Einstein in each otherbit of Einstein in each other, , even if it measures in even if it measures in milligramms!milligramms!

Why this picture? Why this picture? He seems to be less He seems to be less

professorial and happier than professorial and happier than in most other photosin most other photos

The beach looks like Stony The beach looks like Stony Brook (?) Brook (?) where he indeed rented for where he indeed rented for few summers. He was at those beaches few summers. He was at those beaches when was asked to write the famous when was asked to write the famous letter to Roosevelt letter to Roosevelt

We should be happy to see a We should be happy to see a bit of Einstein in each otherbit of Einstein in each other, , even if it measures in even if it measures in milligramms!milligramms!

Why this picture? Why this picture? He seems to be less He seems to be less

professorial and happier than professorial and happier than in most other photosin most other photos

The beach looks like Stony The beach looks like Stony Brook (?) Brook (?) where he indeed rented for where he indeed rented for few summers. He was at those beaches few summers. He was at those beaches when was asked to write the famous when was asked to write the famous letter to Roosevelt letter to Roosevelt

OutlineOutlineThe 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 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 few103

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…

• 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”

Two hydro modes can be excited(from our linearized hydro solution):

a a ``diffuson” a ``diffuson” a soundsound

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

AdS/CFTfrom gravity in AdS5 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 LHCwhat people dream about for LHCexperments -- a black hole formation -- experments -- a black hole formation --

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

thermalization, All information falls into thermalization, All information falls into black hole: only total entropy=area of black hole: only total entropy=area of newly formed b.h.horizon = remains newly formed b.h.horizon = remains ……

what people dream about for LHCwhat people dream about for LHCexperments -- a black hole formation -- experments -- a black hole formation --

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

thermalization, All information falls into thermalization, All information falls into black hole: only total entropy=area of black hole: only total entropy=area of newly formed b.h.horizon = remains newly formed b.h.horizon = remains ……

The first gauge-string duality found in 1997The first gauge-string duality found in 1997

AdS/CFT correpondence known as AdS/CFT correpondence known as ``Maldacena duality”``Maldacena duality”

Along the long path illuminated by Along the long path illuminated by Witten,Polyakov,Klebanov… Witten,Polyakov,Klebanov…

AdS/CFT correpondence known as AdS/CFT correpondence known as ``Maldacena duality”``Maldacena duality”

Along the long path illuminated by Along the long path illuminated by Witten,Polyakov,Klebanov… 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 =g2Nc does not run.

• It lives on the 4-dim boundary of 5-d curved AdS (anti-de-Sitter) 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 e2/hbar c=1/137<<1• Atoms and positronium are weakly bound

E=me(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 g2Nc=Nc>>1 yet AdS/CFT told us charges do not fall and

1s state has energy O(M/sqrt(

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• ds2 =(-dt2+dx1

2 +dx22 +dx3

2 +dz2)/z2 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 effectiveVelocity >>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

• T00 ->d3/r7

Times function of the

Angle which is plotted

On the right

• Previously Callan&Guijosa calculated a scalar ”dilaton image”

• (F =d3/r7 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(g2/4) sqrt(N)/L with self-dual f(g2/4) = f(1/(g2/4)

• We calculated stress tensor from this configuration

• In weakly coupled gauge theory Poynting T0i 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 <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

€

η /s = hbar /4π

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

WORLD

ANTIWORLD

One quark (fisherman) isIn our world,The other (fish) in Antiworld (=conj.amplitude)String connects them and conduct waves in one direction through the black hole

Heavy quark in CFT plasmahas a string deformed by ``hot wind”

Herzog,Yaffe,Gubser…May06

calculated the drag force = momentumFlow down the string

Einstein relation between Drag and diffusion is Fulfilled:But how graviy knows?

from P.Chesler,L.Yaffe(also Gubser et al have detailed papersOn this)

Both groups made amazingly detailedDescription 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 correctEven at micro scales

subsonic

supersonic

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<v(critical) which then gets

classically unstable• Numerical solutions at all v<1

• We get (the first time-dependent) hologramm of falling string by solving linearized Einstein eqn for one (and many) strings and found non-hydrodynamical explosion observed in our 4d world

AdS5

Center=

Extremal b.h.

• Holographic image of a falling string

• (as far as we know the first time-dependent hologramm)

• T00 , Toi

• Cannot be reprensented as

hydrodynamical => anisotropic pressure in the ``comoving frame”

Gravity dual for the heavy ion collisions

• 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)

New meaning of dissipation

• Relaxation=formation of a horizon (trapping surface) where information is lost

• Its area gives the entropy: • (is it true for dynamically stretched t-dependent

horizon? Yes to PJ leading order only) • It returns pure thermal Hawking radiation =>

with hydrodynamical hologramm• W.Israel => collapsing shell gets heated, explains the

origin of entropy production

Another duality for sQGP:electric/magnetic fight

Another duality for sQGP:electric/magnetic fight

Fraction of quasiparticles are magnetically Charged (monopoles and dyons) At T<Tc they somehow (?) make a “dual superconductor”=>confinement.

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 scrreningMasses, Nakamura et al, 2004

My arrow shows the ``self-dual” E=M point

Me>MmElectrricdominated

Me<MmMagneticDominated

At T=0 magneticScreening massIs about 2 GeV(de Forcrand et al)(a glueball mass)

Other data (Karsch et al) better show how MeVanishes at Tc

ME/T=O(g)ES 78MM/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)

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

<- n=2 adjoint

Strong coupling in plasma physics: Gamma= <|Epot|>/<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)

Gas, liquid solid

Gelman,ES,Zahed,nucl-th/0601029

With a non-Abelian color => Wong eqn

So why is such plasma a good liquid? Because of magnetic-bottle trapping:

static eDipole+MPS

+

-

MV

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

Chaotic, regular and escape trajectories for a monopole, all different in initial condition by 1/1000 only!

MD simulation for plasma with monopoles (Liao,ES hep-ph/0611131)

monopole admixture M50=50% etcagain diffusion decreases indefinitely, viscosity does not

€

D∝1/Γ^(0.6 − 0.8)It matters: 50-50 mixture makes the best liquid, as itcreates ``maximal trapping”

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

explained)

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

MD results, with specifiedmonopole fraction

->Stronger coupled ->

Most perfect liquid

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

4pi

From RHIC to LHC:(no answers, only 1bn$ questions)(I don’t mean the price of LHC but ALICE)

From RHIC to LHC:(no answers, only 1bn$ questions)(I don’t mean the price of LHC but ALICE)

Will Will ``perfect liquid``perfect liquid” be still there?” be still there? Is Is jet quenchingjet quenching as strong, especially for as strong, especially for

c,b quark jets and much larger pt?c,b quark jets and much larger pt? Is matter response (conical flow at Is matter response (conical flow at

Mach angle) similar? Mach angle) similar? (This is most sensitive to viscosity…)(This is most sensitive to viscosity…)

Will Will ``perfect liquid``perfect liquid” be still there?” be still there? Is Is jet quenchingjet quenching as strong, especially for as strong, especially for

c,b quark jets and much larger pt?c,b quark jets and much larger pt? Is matter response (conical flow at Is matter response (conical flow at

Mach angle) similar? Mach angle) similar? (This is most sensitive to viscosity…)(This is most sensitive to viscosity…)

ConclusionsConclusions StronglyStrongly coupled coupled

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

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

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

E-flux tubesE-flux tubes

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

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

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

E-flux tubesE-flux tubes

AdS/CFT => natural AdS/CFT => natural applications of string applications of string theory, N=4 SYM is not theory, N=4 SYM is not QCD: nonconfining andQCD: nonconfining and

Strongly coupled, sQGP is OKStrongly coupled, sQGP is OK RHIC data on transport RHIC data on transport

(eta,D), ADS/CFT and (eta,D), ADS/CFT and classical MD all classical MD all qualitatively agree!qualitatively agree!

Are these two Are these two pictures related? pictures related?

AdS/CFT => natural AdS/CFT => natural applications of string applications of string theory, N=4 SYM is not theory, N=4 SYM is not QCD: nonconfining andQCD: nonconfining and

Strongly coupled, sQGP is OKStrongly coupled, sQGP is OK RHIC data on transport RHIC data on transport

(eta,D), ADS/CFT and (eta,D), ADS/CFT and classical MD all classical MD all qualitatively agree!qualitatively agree!

Are these two Are these two pictures related? pictures related?

Good liquid Good liquid because of because of magnetic-magnetic-bottle bottle trappingtrappingClassical Classical MD is being MD is being done,done, the lowest the lowest viscosity for viscosity for 50-50% 50-50% electric/magneelectric/magnetic plasmatic plasma

reservereserve

Effective coupling is large! alphas=O(1/2-1) (not <0.3 as in pQCD applications)

tHooft lambda=g2Nc=4piNc=O(20)>>1-1

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

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): Feynman theory (for liquid He4): polygon jumps polygon jumps BEC if exp(-∆S(jump))>.16 or so (1/NBEC if exp(-∆S(jump))>.16 or so (1/Nnaighboursnaighbours))

Feynman theory (for liquid He4): Feynman theory (for liquid He4): polygon jumps polygon jumps BEC if exp(-∆S(jump))>.16 or so (1/NBEC if exp(-∆S(jump))>.16 or so (1/Nnaighboursnaighbours))

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 above critical

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

Jumping paths:Feynman,interacting

At e=m line both effective gluons and At e=m line both effective gluons and monopoles have masses M about 3T exp(-monopoles have masses M about 3T exp(-3)<<1 is our classical parameter3)<<1 is our classical parameter

(Boltzmann statistics is good enough)(Boltzmann statistics is good enough) At T=Tc monopoles presumably go into Bose-At T=Tc monopoles presumably go into Bose-

Einsetein condensation => new semiclassical Einsetein condensation => new semiclassical theory of it for strongly interacting Bose theory of it for strongly interacting Bose gases, tested on He4gases, tested on He4

(M.Cristoforetti, ES, in progress)(M.Cristoforetti, ES, in progress)

At e=m line both effective gluons and At e=m line both effective gluons and monopoles have masses M about 3T exp(-monopoles have masses M about 3T exp(-3)<<1 is our classical parameter3)<<1 is our classical parameter

(Boltzmann statistics is good enough)(Boltzmann statistics is good enough) At T=Tc monopoles presumably go into Bose-At T=Tc monopoles presumably go into Bose-

Einsetein condensation => new semiclassical Einsetein condensation => new semiclassical theory of it for strongly interacting Bose theory of it for strongly interacting Bose gases, tested on He4gases, tested on He4

(M.Cristoforetti, ES, in progress)(M.Cristoforetti, ES, in progress)

Bose condensation versus repulsive scattering lengthBose condensation versus repulsive scattering length

BEC (confinement) condition for monopolesBEC (confinement) condition for monopolesFor charged Bose gas (monopoles) the action for the jump can be calculated similarly, but For charged Bose gas (monopoles) the action for the jump can be calculated similarly, but

relativistically; jumps in space d and in timerelativistically; jumps in space d and in timeComparable)Comparable)

∆∆S=M sqrt(dS=M sqrt(d22+(1/Tc)+(1/Tc)22)+ ∆S(interaction) = Sc =1.65-1.89)+ ∆S(interaction) = Sc =1.65-1.89(first value from Einstein ideal gas, second from liquid He)(first value from Einstein ideal gas, second from liquid He)

provides the monopole mass M at Tcprovides the monopole mass M at Tc

M Tc approx 1.5 =>M Tc approx 1.5 => M as low as 300 MeVM as low as 300 MeV

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

Comparable)Comparable)

∆∆S=M sqrt(dS=M sqrt(d22+(1/Tc)+(1/Tc)22)+ ∆S(interaction) = Sc =1.65-1.89)+ ∆S(interaction) = Sc =1.65-1.89(first value from Einstein ideal gas, second from liquid He)(first value from Einstein ideal gas, second from liquid He)

provides the monopole mass M at Tcprovides the monopole mass M at Tc

M Tc approx 1.5 =>M Tc approx 1.5 => M as low as 300 MeVM as low as 300 MeV