Heavy ion collisions and AdS/CFT

1. Heavy ion collisions and AdS/CFT Amos Yarom With S. Gubser and S. Pufu.

2. Part 1: Shock waves and wakes.

3. RHIC Au 79 protons 118 neutrons 197 nucleons En = 100 GeV g ~ En/Mn ~ 100

4. RHIC Au 79 protons 118 neutrons 197 nucleons En = 100 GeV g ~ En/Mn ~ 100

5. RHIC t < 0

6. RHIC t > 0 ~ 5000

7. Df dN df RHIC Df

8. 0 p Df dN df RHIC

9. STAR, nucl-ex 0701069

10. 0 p Df dN df RHIC

11. 0 p Df dN df RHIC

13. RHIC

14. 0 p Df dN df q RHIC cs/v=cos q

16. 0 p Df dN df RHIC

17. Casalderrey-Solana et. al. hep-ph/0411315 0 p Df dN df I I II II

18. Casalderrey-Solana et. al. hep-ph/0411315 I II

19. AdS space 0 z

20. AdS-Schwarzschild z0 0 z

21. AdS-Schwarzschild Conformal invariance: Large N: So: What we expect for the stress tensor:

22. AdS-Schwarzschild Rewrite the metric in the form: The boundary theory stress tensor is given by: Computing the stress tensor:

23. AdS-Schwarzschild To convert from the z to the y coordinate system: Recall that we need: So we can compute:

24. AdS-Schwarzschild We find: Using the AdS/CFT dictionary: We obtain: From: and

25. AdS-Schwarzschild 0 z0 z

26. A moving quark 0 Consider a `probe quark’. It’s profile will be given by the solution to the equations of motion which follow from: z0 z A quark is dual to a string whose endpoint lies on the boundary ?

27. A moving quark Consider the ansatz: We can easily evaluate: The string metric is:

28. A moving quark

29. A moving quark Notice that since the Lagrangian is independent of x, then Inverting this relation we find: is conserved.

30. A moving quark Requiring that implies that the numerator and denominator change sign simultaneously. Defining: Then:

31. A moving quark v ? 0 z0 z

32. The metric backreaction The equations of motion are: where: The total action is + equations of motion for the string.

33. The metric backreaction The AdS/CFT dictionary gives us: So We work in the limit where: where:

34. The metric backreaction We work in the limit where: where:

35. The metric backreaction To leading order: Whose solution is We work in the limit where:

36. The metric backreaction We work in the limit where: Whose solution is

37. The metric backreaction At the next order: • Work in Fourier space: • Fix a gauge: • Use the symmetries: We make a few simplifications:

38. The metric backreaction At the next order: Using: we can obtain: We eventually must resort to Numerics.

39. Energy density

40. Energy density

41. Energy density

42. Near field energy density

43. The Poynting vector

44. I II

45. 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.

46. I II

47. Noronha et. al. Used a hadronization algorithm to obtain an azimuthal distribution of a “hadronized” N=4 SYM plasma.

48. References • 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. 0901.0230Reviews.