AdSCFT Calculations of Parton Energy Loss

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AdS/CFT Calculations of Parton Energy Loss

• Jorge Casalderrey-Solana
• Lawrence Berkeley National Lab.

In collaboration with D. Teaney
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Why N 4 Yang Mills?
The QGP at T(1-2)Tc may be strongly coupled
Strong flow observed at RHIC consistent with
ideal hydro.
Estimates and calculations on QGP shear
viscosity yield small values.
Transport requires cross sections 10 times larger
than pQCD.
Strong jet quenching (opaque medium).
as(T) is large.
N4 Yang Mills can be solved at strong coupling
via AdS/CFT
Pressure at strong coupling is ¾
PStephan-Boltzmann .
Lattice QCD? similar deviations are observed at
T(1-2)Tc .
Shear viscosity conjectured
minimal bound.
Non perturbative access to real time dynamics of
gauge theories.
But N4 is not QCD (scale invariant,
supersymmetry)
However AdS/CFT is the only method available to
address strongly coupled gauge theories
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Density Matrix of a Heavy Quark
Eikonalized ? EgM gtgt T
momentum change
medium correlations
observation
Fixed gauge field ? propagation color rotation
Evolution of density matrix
Un-ordered Wilson Loop!
Introduce type 1 and type 2 fields as in
no-equilibrium and thermal field theory
(Schwinger-Keldish)
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Momentum Broadening
Transverse momentum transferred
Transverse gradient ? Fluctuation of the Wilson
line
Four different correlators
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Wilson Line From Classical Strings
Heavy Quark ? Move one brane to 8.
The dynamics are described by a classical
string between black and boundary barnes
Nambu-Goto action ? minimal surface with boundary
the quark world-line.
If the branes are not extremal they are black
branes? horizon
Which String Configuration corresponds to the 1-2
Wilson Line?
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Kruskal Map
Black hole ? two copies of the (boundary) field
theory (Maldacena)
Each (boundary) fields are identified with type 1
and 2.
Herzog Son Fluctuations on (R, L) can be
matched so that field correlators have the
correct analytic properties (KMS relations)
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Fluctuations (static) of the Quark World Line
Small fluctuation problem (linearized)
Near the horizon (u?1/r20)
infalling
outgoing
Son-Herzog prescription
KMS relation (static quarks in equilibrium)
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Consequences for Heavy Quarks
Heavy probe on plasma gt Brownian Motion
(Langevin dynamics)
HQ Diffusion coefficient (Einstein)
Putting numbers
It is not QCD but QCD at weak coupling
Different number of degrees of freedom
Liu, Rajagopal, Wiedemann
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Drag Force
(Herzog, Karch, Kovtun, Kozcaz and Yaffe
Gubser)
Langevin
Einstein relation
Direct computation HQ forced to move with
velocity v
? Wilson line xvt at the boundary
v
Add an external electric field to valance the drag
Energy and momentum flux through the string
same k !
Fluctuation-dissipation theorem
Drag force valid for ultra relativistic particle.
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Broadening of a Fast Probe
Fluctuations of the bending string
Complications
Discontinuity in the past horizon
World sheet horizon at
New Scale!
Similar to KMS relation but GR is
infalling in the world sheet horizon The
temperature of the correlator is that of the
world sheet black hole
(blue shift?)
Diverges in ultra relativistic limit!
But the brane does not support arbitrary large
electric fields (pair production)
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Computation of (Radiative Energy Loss)
(Liu, Rajagopal, Wiedemann)
Dipole amplitude two parallel Wilson lines
in the light cone
Order of limits
String action becomes imaginary for
For small transverse distance
entropy scaling
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Conclusions
AdS/CFT provides a rigorous way to address the
physics at strong coupling.
The computed transport coefficient have
remarkable features
Large values Unusual coupling dependences Energy
dependence of the momentum broadening
Many other application of AdS/CFT to Heavy Ion
phenomenology (fields associated to probe,
hydrodynamics, production of fireball)
The applicability of these results demand
phenomenological work to explain them in a way
which can be translated to QCD.
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Boundary Conditions for Fluctuations
Son, Herzong (Unruh)
Negative frequency modes
near horizon
?
Positive frequency modes
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Fluctuations of moving string
String solution at finite v
discontinous across the past horizon (artifact)
Small transverse fluctuations in (t,u) coordinates
Both solutions are infalling at the AdS horizon
Which solution should we pick?
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World Sheet Horizon
We introduce
Same as v0 when
The induced metric is diagonal
World sheet horizon at
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Fluctuation Matching
The two modes are infalling and outgoing in the
world sheet horizon
Close to V0 both behave as v0 case ? same
analyticity continuation
The fluctuations are smooth along the future
(AdS) horizon.
(prescription to go around the
pole)