7/28/2019 Chiral Magnetic Effect

1/14

The chiral magnetic effect in stronglycoupledanisotropic plasma

Ilmar Gahramanov

DESY Hamburg, Germany

Talk is based on

I.G., Tigran Kalaydzhyan, Ingo Kirsch arXiv:1203.4259

INTERNATIONAL SCHOOL OF SUBNUCLEAR PHYSICSErice, 25 June 2012

http://find/

7/28/2019 Chiral Magnetic Effect

2/14

Motivation

The chiral magnetic effect represents remarkable implications of anomalies in QFT

The chiral magnetic effect is a good candidate for the explanationof an experimentally observed charge asymmetry in heavy-ioncollisions at RHIC

Lattice QCD results suggest the existence of the effect

http://find/

7/28/2019 Chiral Magnetic Effect

3/14

Chiral magnetic effect

The CME is a hypothetical phenomenon which states that, in thepresence of a magnetic eld B , an electric current is generatedalong B in the background of topologically nontrivial gluon elds.

j = C5 B [Kharzeev,Fukushima,Warringa,Mclerran]

http://goforward/http://find/http://goback/

7/28/2019 Chiral Magnetic Effect

4/14

Basics of relativistic hydrodynamics

Hydrodynamics states is completely determined by conservation lawsassociated with some global symmetries

T = 0 j = 0

In equilibrium, for ideal hydrodynamics

T = ( + P )u u

P g

j = u

http://find/

7/28/2019 Chiral Magnetic Effect

5/14

build up of elliptic flow

P T P L

plasma phase mixed phase hadronic gas phase

v

0 2 4 6 8 10 12 fm0.00

0.02

0.04

0.06

0.08

0.10

0.12

p

Why the anisotropic case interesting?Experimental observation: The charge separation is proportionalto the elliptic ow v2 .

http://find/

7/28/2019 Chiral Magnetic Effect

6/14

Anisotropic uidStress-energy tensor T and U (1) currents j :

T = ( + P T )u u + P T g (P T P L )v v + j = u +

In the rest frame

T =

0 0 00 P T 0 00 0 P T 00 0 0 P L

In presence of anomalies one need to modify the dissipative part of the current

j j + + B B

These transport coefficients can be computed exactly.

[Erdmenger,Haack,Kaminski,Yarom '08]

[Son & Surowka '09]

http://find/

7/28/2019 Chiral Magnetic Effect

7/14

In presence of external elds

Now the energy-momentum tensor and current are not conserved

T = F a j a j a = C abc E b B c

2nd law of thermodynamicsPositivity of the entropy production completely xes new transportcoefficients

= C 2 23 3

+ P T + O(T 2)

B = C 12

2

+ P T + O(T 2)

http://find/

7/28/2019 Chiral Magnetic Effect

8/14

Two charge case

Isotropic case [Sadofyev,Isachenkov 10] For an anisotropic case the conductivities

= 2 C 5

+ P T 2 +

253

B = C 5 1

+ P T

5 ,B = C 1 1

2

+ P T

1 +25

3 2

We expand the CME-coefficient B to linear order in p

B C5 1 + P

1 p16

http://find/

7/28/2019 Chiral Magnetic Effect

9/14

Holographic principle

Holographic principleAny theory of quantum gravity in (d + 1) dimensions has a dualdescription in terms of a QFT without gravity in d dimensions

In its most familiar example, the AdS/CFT correspondence, thequantum theory of gravity is string theory on asymptotically AdSspace , and the theory on the boundary is a conformal eld theory .

Hydrodynamic approximation

Duality between the long wavelength asymptotically AdS planarblack hole solution of the EinsteinMaxwell theory with negativecosmological constant and the equations of charged uid dynamics

http://find/

7/28/2019 Chiral Magnetic Effect

10/14

Gravity computation

We start from a ve-dimensional U (1) n Einstein-Maxwell theory in anasymptotic AdS space

S =1

16G 5 d5x g[R 2 F

aMN F

aMN

+S abc

6 g PKLMN

AaP F

bKL F

cMN

information about triangle anomalies]

Solution of the equations of motion: AdS black hole withU (1) V U (1) A

http://find/

7/28/2019 Chiral Magnetic Effect

11/14

Gravity computationAn ansatz for an anisotropic AdS black hole solution

ds2 =

f (r )dt2 + 2 drdt + r 2(wT (r )dx2 + wT (r )dy2 + wL (r )dz2)

Aa = Aa0 (r )dtAn asymptotic solution ( r )

Aa

0 (r ) = a +

3q a2r 2 + O(r

8

) wT (r ) = 1 +w(4)T r 4 + O(r

8

)

f (r )/r 2 = 1 mr 4

+a

(q a )2

r 6+ O(r

8) wL (r ) = 1 +w(4)Lr 4

+ O(r 8)

Transverse and longitudinal pressures

P T =m 4w

(4)T 4w

(4)L

16G 5=

m(1 + )16G 5

P L =m 8w

(4)T

16G 5=

m(1 2 )16G 5

http://find/

7/28/2019 Chiral Magnetic Effect

12/14

A roadmap of computation

Vary 4-velocity and background elds up to rst order

Solve equations of motion and nd the rst-order corrections Read off U (1) currents from the near-boundary expansion of the

rst-order corrected background

http://find/

7/28/2019 Chiral Magnetic Effect

13/14

Comparing apples to oranges

024

68

101214161820

0 2 4 6 8 10 12

w L

( r +

)

anisotropy

hydrodynamics

holography, numerics

Comparing

j a =1

16G 5 Qa (r + ) + r + A

a0

(r + )C

with the general expansion

j a = a u u + abB

u

Ab

http://find/

7/28/2019 Chiral Magnetic Effect

14/14

The transport coefficients from gravity

a =4

16G 5S abc bc

23

a

+ P T S bcd bc d

abB = 416G 5S abc c 12

a

+ P T S bcd c d

Vi ringrazio per lattenzione!

http://find/