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

~ En/Mn ~ 100

RHIC

Au

79 protons

118 neutrons

197 nucleons

En = 100 GeV

~ En/Mn ~ 100

RHIC

t < 0

RHIC

t > 0

~ 5000

RHIC

ddN

RHIC

ddN

0

STAR, nucl-ex 0701069

RHIC

ddN

0

RHIC

ddN

0

RHIC

RHIC

cs/v=cos

ddN

0

RHIC

ddN

0

Casalderrey-Solana et. al. hep-ph/0411315

ddN

0

I

I

II

II

Casalderrey-Solana et. al. hep-ph/0411315

I II

AdS space

z

0

AdS-Schwarzschild

z

0

z0

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-SchwarzschildTo convert from the z to the y coordinate system:

Recall that we need: So we can compute:

AdS-SchwarzschildFrom: and

We find:

Using the AdS/CFT dictionary:

We obtain:

AdS-Schwarzschild

z

0

z0

A moving quark

z

0

z0

?

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

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

z0

? v

The metric backreactionThe 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

Energy density

Energy density

Near field energy density

The Poynting vector

I II

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,

I II

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

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. 0901.0230 Reviews.