AdSCFT Applications

1
AdS/CFTApplications

• Jorge Casalderrey-Solana
• LBNL

2
Langevin Model for Heavy Quarks
Heavy Quark with vltlt1? neglect radiation
? HQ classical on medium correlations scale
? white noise ?
Einstein relations
3
Noise from Microscopic Theory
HQ momentum relaxation time
Consider times such that

microscopic force (random)
?
charge density
electric field
Convenient rewriting
?
4
Force Correlators from Wilson Lines
Integrating the Heavy Quark propagator
Which is obtained from small fluctuations of the
Wilson line
5
Adding Temperature and Heavy Quarks
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.
Wilson Line
If the branes are not extremal they are black
branes? horizon
The Hawking temperature of the brane becomes the
temperature of the FT
6
Fluctuations of the Quark World Line
Prescription for retarded correlators
Solve the linearized equations of motion
Impose infalling boundary conditions at the
horizon
The retarded correlator is given by the boundary
action
7
Drag Force
(Herzog, Karch, Kovtun, Kozcaz and Yaffe
Gubser)
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
Drag force valid for ultra relativistic particle!
Einstein relations
same k !
Fluctuation-dissipation theorem
8
Consequences for Heavy Quarks
Heavy probe on plasma gt Brownian Motion
(Langevin dynamics)
HQ Diffusion coefficient (Einstein)
From Rapps talk
Different number of degrees of freedom
But, for the Langevin process to apply
9
Broadening of a Fast Probe
Fluctuations of the bending string
Complication
World sheet horizon at
v
New Scale!
Similar 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)
10
Back Up
11
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
12
Momentum Broadening
Transverse momentum transferred
Transverse gradient ? Fluctuation of the Wilson
line
Four different correlators
13
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)
14
Boundary Conditions for Fluctuations
Son, Herzong (Unruh)
Negative frequency modes
near horizon
?
Positive frequency modes
15
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?
16
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)