1. Studying the strongly coupled N=4 plasma using AdS/CFT
Amos Yarom, Munich
Together with S. Gubser and S. Pufu
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2. Calculating the stress-energy tensor
AdS/CFT
J. Maldacena
 >> 1
N >> 1

3. Calculating the stress-energy tensor
Anti-de-Sitter space.
Strings in Anti-de-Sitter space.
The energy momentum tensor via AdS/CFT.
Results.

4. Flat space ds2 = c2 dx2+c2 dy2+c2 dz2 ds2 = dx2 + dy2 + dz2 + dw2
- dt2 y
x  c x
y  c y
z  c z
ds2
dx2
dy2
dz2 x z

5. 5d Anti de-Sitter space
ds2 =L2 z-2 (dz2+dx2+dy2+dw2 - dt2) + z

6. AdS5 black hole
ds2 =L2 z-2 (dz2/(1-(z/z0)4)+dx2+dy2+dw2 - (1-(z/z0)4) dt2)
ds2 = gdxdx z0 z

7. Strings in AdS ds2 = gdxdx ______ √g ( X)2 d d SNG= s X()1
___
20 z z0
X()
X(,t) 

8. N=4 SYM plasma via AdS/CFT
J. Maldacena
AdS5
CFT
Empty AdS5
Vacuum
L4/’2
gYM2 N
 L3/2 G5 N2
J. Maldacena hep-th/

9. N=4 SYM plasma via AdS/CFT
Empty AdS5
AdS5 BH
Thermal state
Vacuum
L4/’2
gYM2 N
 L3/2 G5 N2
Horizon radius
Temperature
J. Maldacena hep-th/
E. Witten hep-th/

10. Static ‘quarks’ using AdS/CFT
AdS5
CFT
J. Maldacena hep-th/
Massive particle
Endpoint of an open string on the boundary
AdS/CFT
J. Maldacena ? z0 z
 SNG
 X =0

11. Moving ‘quarks’ using AdS/CFT
AdS5
CFT
J. Maldacena hep-th/
Massive particle
Endpoint of an open string on the boundary ? z0 z
 SNG
 X =0

12. Moving ‘quarks’ using AdS/CFT
AdS5
CFT
J. Maldacena hep-th/
Massive particle
Endpoint of an open string on the boundary z0 z
 SNG
 X =0

13. Extracting the stress-energy tensor using AdS/CFT
AdS5
CFT
gmn|b
<Tmn>
E. Witten hep-th/ z0 z

14. Extracting the stress-energy tensor using AdS/CFTz0 z
AdS5
CFT
gmn|b
<Tmn>
E. Witten hep-th/
ds2 = gdx dx
g = gAdS-BH+h
Metric fluctuations
AdS black hole

15. The energy momentum tensor
(Friess, Gubser, Michalogiorgakis, Pufu, hep-th/ )
g=gAdS+ h z0 z

16. Energy density for v=3/4 Over energy Under energy
(Gubser, Pufu, AY, ArXiv: , Chesler, Yaffe, ArXiv: )
Over energy
Under energy

17. v=0.75
v=0.58
v=0.25

18. Small momentum approximations
(Friess, Gubser, Michalogiorgakis, Pufu, hep-th/ )

19. Small momentum approximations
(Gubser, Pufu, AY, ArXiv: )
1-3v2 < 0 (supersonic)
1-3v2 > 0 (subsonic)

20. Small momentum approximations
(Gubser, Pufu, AY, ArXiv: )

21. Small momentum approximations
(Gubser, Pufu, AY, ArXiv: )
s=1/3
cs2=1/3

22. Energy density for v=3/4

24. v=0.75
v=0.58
v=0.25

25. Large momentum approximations
(Gubser, Pufu hep-th: AY, hep-th: )

26. Large momentum approximations
(Gubser, Pufu hep-th: AY, hep-th: )

27. The Poynting vector S1 S? V=0.25 V=0.58 V=0.75
(Gubser, Pufu, AY, ArXiv: ) S1 S?
V=0.25
V=0.58
V=0.75

28. Small momentum asymptotics
(Gubser, Pufu, AY, ArXiv: )
Sound
Waves ?

29. Small momentum asymptotics
(Gubser, Pufu, AY, ArXiv: )

30. The poynting vector S1 S? V=0.25 V=0.58 V=0.75
(Gubser, Pufu, AY, ArXiv: ) S1 S?
V=0.25
V=0.58
V=0.75

31. Energy analysis
(Friess, Gubser, Michalogiorgakis, Pufu, hep-th/ ,
Gubser, Pufu, AY, ArXiv: , )

32. Energy analysis
(Friess, Gubser, Michalogiorgakis, Pufu, hep-th/ ,
Gubser, Pufu, AY, ArXiv: , ) F z0 z
(Herzog, Karch, Kovtun, Kozcaz, Yaffe, hep-th: ,
Gubser, hep-th: )

33. Energy analysis
(Friess, Gubser, Michalogiorgakis, Pufu, hep-th/ ,
Gubser, Pufu, AY, ArXiv: , )

34. Energy analysis
(Friess, Gubser, Michalogiorgakis, Pufu, hep-th/ ,
Gubser, Pufu, AY, ArXiv: , ) S1

35. Summary
AdS/CFT enables us to obtain the energy momentum tensor of the plasma at all scales.
A sonic boom and wake exist.
The ratio of energy going into sound to energy going into the wake is 1+v2:-1.

36. The energy momentum tensor
Cylindrical symmetry
Gauge choice
Tensor modes
Vector modes

37. The energy momentum tensor
Tensor modes
Vector modes
+ first order constraint

38. The energy momentum tensor
Tensor modes
Vector modes
Scalar modes
+ first order constraint
+ 3 first order constraints

39. Large momentum approximations

40. Large momentum approximations