Transcript Gauge-String Duality in Heavy

Heavy ion collisions and AdS/CFT
Amos Yarom
With S. Gubser and S. Pufu.
Part 1:
Shock waves and wakes.
RHIC
Au
79 protons
118 neutrons
197 nucleons
En = 100 GeV
g ~ En/Mn ~ 100
RHIC
Au
79 protons
118 neutrons
197 nucleons
En = 100 GeV
g ~ En/Mn ~ 100
RHIC
t<0
RHIC
t>0
~ 5000
dN
df
RHIC
Df
Df
dN
df
RHIC
0
p
Df
STAR, nucl-ex 0701069
dN
df
RHIC
0
p
Df
dN
df
RHIC
0
p
Df
RHIC
dN
df
RHIC
cs/v=cos q
0
q
p
Df
dN
df
RHIC
0
p
Df
Casalderrey-Solana et. al. hep-ph/0411315
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II
dN
df
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II
0
p
Df
Casalderrey-Solana et. al. hep-ph/0411315
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II
AdS space
0
z
AdS-Schwarzschild
0
z0
z
AdS-Schwarzschild
What we expect for the stress tensor:
Conformal invariance:
Large N:
So:
AdS-Schwarzschild
Computing the stress tensor:
Rewrite the metric in the form:
The boundary theory stress tensor is given by:
AdS-Schwarzschild
To convert from
the z to the y
coordinate system:
Recall that we need:
So we can compute:
AdS-Schwarzschild
From:
and
We find:
Using the AdS/CFT dictionary:
We obtain:
AdS-Schwarzschild
0
z0
z
A moving quark
0
?
A quark is dual to a string
whose endpoint lies on the
boundary
z0
z
Consider a `probe quark’. It’s profile will be given by
the solution to the equations of motion which follow
from:
A moving quark
Consider the ansatz:
We can easily evaluate:
The string metric is:
A moving quark
A moving quark
Notice that since the Lagrangian is independent of x, then
is conserved. Inverting this relation we find:
A moving quark
Requiring that
implies that the numerator and
denominator change sign simultaneously.
Defining:
Then:
A moving quark
0
?
z0
z
v
The metric backreaction
The total action is
The equations of motion are:
where:
+ equations of motion for the string.
The metric backreaction
where:
The AdS/CFT dictionary gives us:
So
We work in the limit where:
The metric backreaction
where:
We work in the limit where:
The metric backreaction
We work in the limit where:
To leading order:
Whose solution is
The metric backreaction
We work in the limit where:
Whose solution is
The metric backreaction
At the next order:
We make a few simplifications:
•Work in Fourier space:
•Fix a gauge:
•Use the symmetries:
The metric backreaction
At the next order:
We eventually must resort to Numerics. Using:
we can obtain:
Energy density
Energy density
Energy density
Near field energy density
The Poynting vector
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II
Some universal properties
These results remain unchanged even if we add scalar matter,
They also remain unchanged if the string is replaced by
another object that goes all the way to the horizon.
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II
Noronha et. al. Used a hadronization
algorithm to obtain an azimuthal
distribution of a “hadronized” N=4 SYM
plasma.
References
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STAR collaboration nucl-ex/0510055, PHENIX collaboration 0801.4545. Angular correlations.
Casalderrey-Solana et. al. hep-ph/0411315. Shock waves in the QGP.
Gubser hep-th/0605182, Herzog et. al. hep-th/0605158. Trailing strings.
Friess et. al. hep-th/0607022, Yarom. hep-th/0703095, Gubser et. al. 0706.0213, Chesler et. al.
0706.0368, Gubser et. al. 0706.4307, Chesler et. al. 0712.0050. Computing the boundary theory
stress tensor.
Gubser and Yarom 0709.1089, 0803.0081. Universal properties.
Noronha et. al. 0712.1053, 0807.1038, Betz et. al. 0807.4526. Hadronization of AdS/CFT result.
Gubser et. al. 0902.4041, Torrieri et. al. 0901.0230 Reviews.