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

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Presentation transcript:

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 E n = 100 GeV  ~ E n /M n ~ 100

RHIC Au 79 protons 118 neutrons 197 nucleons E n = 100 GeV  ~ E n /M n ~ 100

RHIC t < 0

RHIC t > 0 ~ 5000

RHIC  dd dN

RHIC  dd dN 0 

STAR, nucl-ex

RHIC  dd dN 0 

RHIC  dd dN 0 

RHIC

c s /v=cos   dd dN 0  

RHIC  dd dN 0 

Casalderrey-Solana et. al. hep-ph/  dd dN 0  I I II

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

AdS space z 0

AdS-Schwarzschild z 0 z0z0

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 z 0 z0z0

A moving quark z 0 z0z0 ? Consider a `probe quark’. It’s profile will be given by the solution to the equations of motion which follow from: A quark is dual to a string whose endpoint lies on the boundary

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

A moving quark

Notice that since the Lagrangian is independent of , 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 z 0 z0z0 ? 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 We make a few simplifications: Work in Fourier space: Fix a gauge: At the next order: Use the symmetries:

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

Energy density

Near field energy density

The Poynting vector

III

Some universal properties They also remain unchanged if the string is replaced by another object that goes all the way to the horizon. These results remain unchanged even if we add scalar matter,

III

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

References STAR collaboration nucl-ex/ , PHENIX collaboration Angular correlations. Casalderrey-Solana et. al. hep-ph/ Shock waves in the QGP. Gubser hep-th/ , Herzog et. al. hep-th/ Trailing strings. Friess et. al. hep-th/ , Yarom. hep-th/ , Gubser et. al , Chesler et. al , Gubser et. al , Chesler et. al Computing the boundary theory stress tensor. Gubser and Yarom , Universal properties. Noronha et. al , , Betz et. al Hadronization of AdS/CFT result. Gubser et. al , Torrieri et. al Reviews.