Holographic Energy Loss.
Herzog, AK, Kovtun, Kozcaz, Yaffe, JHEP 0607 (2006) 013
Chesler, Jensen, AK, Yaffe, Phys.Rev. D79 (2009) 125015
Janiszewski, AK, arxiv:1106.4010

Introduction andMotivation
Can stringy theory help to understandheavy ion collisions (RHIC,LHC) ?

RHIC…. bird’sperspective

RHIC:…. experimentalistsperspective.

RHIC:…. string theorist’s perspective.

Science at RHIC:
Collides high energy gold nuclei.
Goal: Study Thermodyamics andHydrodynamics of QCD at temperaturesof order QCD
Thermo: Equilibrium Properties
Hydro: effective theory describing small, longwavelength fluctuations around equilibriumQCD Thermodynamics
and Hydrodynamics.

QCD thermodynamics:
QCD thermodynamics is under good theoreticalcontrol using lattice gauge theory.
Borsanyi et al, hep-lat/0106019

Pressure (T)(2+1 flavors)

What do we know about QCD thermo?
sb, ssb : entropy/energy
density of free gas.
at very large T thecoupling goes to zero,so s has to become ssb
at T ~ QCD

free gas with smallish
residual interactions?

Near Equilibrium Dynamics:
Fireball at best in local equilibrium!
Theoretically only very poorly understood.
Hydro: effective theory describing small, longwavelength fluctuations around equilibrium
Hydro degrees of freedom: conserved charges!
present in any theory: , iHydro as an effective theory
Hydro equations of motion:(conservation laws)
Speed of soundand constitutive relations:
Energy density

Pressure

Shear viscosity

Momentum density

Kubo Formulas.

(from Arnold, Moore & Yaffe)

Shearviscosity

Stress-Energy
2-pt function.

Need correlation
functions in microscopic theory.

Drag on a heavy quark.
Another interesting hydrodynamic quantity
in QCD is the drag force excerted on a quark.
Energetic quarks see “interior” of fireball.

Also can be obtained from a correlation
function via a Kubo formula (Solana-Teaney)

QCD Hydro from the lattice?
These are real time correlation functions!
Non-equilibrium physics, real time fluctuations
around thermal equilibrium.
Extremely difficult on the lattice, since latticegauge theory is tied to a Euclidean formulation.

QCD Hydro from perturbation theory?
Of course at very high T (weak coupling)
everything is under control…
At weak coupling transport coefficients canbe calculated using perturbation theory.
(Actual calculation by Arnold, Moore and Yaffe
first matches to Boltzman equation and then toHydro)

Weak Coupling Results(Arnold, Moore & Yaffe) depends on
Nf and Nc

Note that the viscosity goes up as the couplinggoes to zero!!

Weak Coupling Results
The drag on a heavy quark on the other handgoes to zero as we turn of the coupling.
Explicit formulas have been worked out by
Moore and Teaney .

Summary: Theory Expectations
At asymptotically large Temperature:
Stefan-Boltzman thermodynamics
large viscosity
no drag(free) Quark Gluon Plasma
Pre-RHIC believe: around T=Tc qualitatively
similar behavior, e.g. s ~ ¾ sSB

Hydro and Thermo atRHIC

Experimental Surprises at RHIC
The system thermalizes rapidly Hydrodynamic simulations work extremely
well and indicate low viscosity ( ~ 0)(elliptic flow)
 Quarks experience a strong drag force in the“plasma” (elliptic flow, jet-quenching).
“strongly coupled quark gluon plasma”,“quark gluon liquid”

Elliptic flow.

Au

Au

How does the almondshaped fluid expand?

low pressurehigh pressure

Elliptic flow.

(Cold atomic gas, Ketterle group, MIT)What do we learn from elliptic flow?
Hydrodynamic modelling works wellafter short thermalization time with basically zero viscosity
 for light and heavy quarks (“charm goeswith the flow”); implies large drag forheavy quarks
Jet quenching.
See one of two back-to-backcreated particles.
The other one got “stuck” in the fireballJet quenching is a direct indication of large dragalso for light quarks.

Jet Quenching at the LHC (Atlas)(fist time actually single jet was reconstructed, RHIC only studied 2-particle
correlations

Stopping Distance:
For light quarks better question:
How far does quark of energy E travel before
it gets thermalized into the plasma?

Perturbative QCD:
Experiment:

L ~ E1/2(BDMPS, …)

L ~ E1/3 gives slightly(Renk, …)
better fit

Holography

Can we calculate transport coefficientsin any strongly coupled field theory?
N=4 SYM at strong ‘t Hooft coupling!

AdS/CFT allows us to perform all the microscopic
calculations using classical gravity in the 5d dual.
Only known “first principle” calculation of hydroat strong coupling.

What can we learn from N=4 SYM?
It can teach us qualitatively what are typical valuesof viscosity and drag in a strongly coupled plasma.
N=4 is the only theory in which we can calculate,so we should!
Since hydro is largely insensitive to microscopic
details one could hope for some “universality” thatall strongly coupled plasmas are the “same” and doquantitative comparisons.

N=4 thermo and hydro.
(Gubser, Klebanov, Peet)

Thermo:Hydro:(Kovtun, Son, Starinets)

Fits data better than 0
but also better thanextrapolated PT.

Holographic Quarks.
open
strings
closedstrings

horizon(AK, Ami Katz)(Sakai, Sugimoto)

Quarks (N=2 hypers)
can be simply
incorporate into any
background using flavor
branes (D7 branes).
 Flavor brane terminates
at a position determinedby its mass.
 Open strings = Mesons
 Baryons = soliton.
Quarks in N=4 SYM.
open
strings

horizonumFlavored Quasiparticle
can be introduced bysemi-classic string.
 Describes Quark andsurrounding Plasma
cloud.

uh

Mass >> TemperatureQuarks in N=4 SYM.
openstringschorizonuhFlavored Quasiparticle
can be introduced bysemi-classic string.
 Describes Quark andsurrounding Plasma
cloud.
Mass << Temperature

Heavy Quark Energy LossDrag for a stationary solution. (HKKKY, Gubser)
Constant E - fieldv

momentum flows
at constant rate.

World-Sheet Horizon

gluon tail
Loss rate:

rate at which the external
field does work.

Drag for a stationary solution.
Velocity dependece simply fromblueshifted energy density.

/in d dimensions(HKKKY)

Loss rate:

Temperature dependence
determined by dimensional analysis

Energy and Momentum Density(Chesler and Yaffe)Small fluctuations:
A lot of extra information in small fluctuations
around the dragging string solution:• Relaxation Times• Momentum Broadening (transverseand longitudinal)• Brownian Motion = Hawking
Radiation• …..
(HKKKY, ……., Shigemori, …..)Light Quark Energy Loss
(Chesler, Jensen, Karch, Yaffe)Holographic Image (zero T):

Two “blobs” of energy density / charge density
rushing apart and expanding.
“SHOWERING”

Quasi-Particle excitations.

Zero TJets

Quasiparticle in Plasma(for E >> T)

FinalDiffusion

Quasi-Particle excitations.

Numeric Solution

Approximate Solution
for E >> TJet in N=4 SYM:

Light Quark Stopping Distance
Stopping
Distance:
LMax ~ E1/3

but strong dependence
on details of initial stateDependence on Initial Data
Quasi-Particle = Parton + Soft Gluon Cloud= Initial Shape of String

Stopping Distance depends on details ofgluon cloud!
Need to understand production mechanism.

Holographic 3-pt functions (Arnold, Vaman)
We need to understandbetter how thequasiparticle was createdHolographic 3-pt functions (Arnold, Vaman)
In the realworld:

Formally:

Thermal 3-pt function(can be done holographically)

Stopping distanceExperiment?

agrees with us on maximal
stopping distanceDragging SheetsDragging Sheets(Janiszewski and Karch)v
Worldvolume Horizon

Only sensitive to blue-shifted energy density?
Inhomogeneities?

50

Loss Rate:n: spatial dimensions of defectd: space-time dimensions of the field theoryEnergy(time * volume)=

Only sees blueshifted density!

Induced Horizons.
Moving defects induce worldvolume horizons
even in the absence of spacetime horizons.
(see also Das, Nishioka, Takayanagi and Frolov, Mukohyama)

Higher dimensional defects allow moreinteresting induced gravitational phenomena.

World-volume Hawking-Page

SlowFastWorld-volume Hawking-Page(M2 in AdS7)
BowlConeTube

World-volume FRW Universe

Big Bang

FRW Universe

Conclusion (1/2)
Holography provides solvable toy modelsof strong coupling dynamics.
Energy Loss qualitatively different fromweak coupling.

Conclusion (2/2)
By studying higher dimensional defects we can:• confirm the lack of structure instrongly coupled energy loss
• produce tractable world-volume
analogs of curved spacetimes withhorizons
Next: Fluctuations? Turbulence?