Ⅱ-5. Hadron Physics (Theory)

RIKEN Accel. Prog. Rep. 47 (2014)

Out-of-equilibrium chiral magnetic effect at strong coupling†
S. Lin ∗1 and H-U. Yee∗1,∗2
The chiral magnetic effect in relativistic heavy-ion
collisions has been proposed as a signature of local
parity violation in QCD above deconfinement phasetransition1) . The manifestation of the chiral magnetic
effect requires both a strong magnetic field and chiral imbalance in fundamental quarks. Despite continuous theoretical efforts in understanding the effect,
many quantitative questions remain unanswered. Oneof them is the value of the chiral magnetic conductivity, which is complicated by the fact that the magnetic field produced by the spectators exists only at theearly stage of the collisions, when quark-gluon plasma(QGP) is not yet thermalized. An accurate calculationof the chiral magnetic conductivity should be carriedout for QGP in an out-of-equilibrium setting. In thiswork, we report on our attempt in this direction
We considered chirally imbalanced QGP undergoing
thermalization. It can be modeled by a gravitationallycollapsing shell in 5D Anti-de Sitter (AdS) space. The
shell carries an axial charge density, described by anaxial chemical potential µA . The end point of the gravitational collapse is the formation of the AdS-ReissnerNordstrom (AdS-RN) black hole, which is dual to QGP
with an axial charge density. The central quantity is
the chiral magnetic conductivity in the thermalization
process. It is defined for at finite frequencies as the response of the vector current to the external magneticfield�J�EM = σχ (ω)B(ω).

(1)

This is to be evaluated at different times in the thermalization history. Note that (1) assumes the current
response is much faster than the evolution of QGP
toward equilibrium, which is not true in the nearequilibrium regime. We restricted our study to the farfrom equilibrium regime. We obtained the chiral magnetic conductivity for different frequencies in Fig. 1.
The end point QGP has a temperature T = 300 MeV
and an axial chemical potential µA = 50 MeV. We
found that in general the chiral magnetic conductivity
increases as QGP thermalizes, which is consistent withthe expectation that more and more thermalized constituents are available in conducting the current. Wealso found that the magnitude of conductivity changes
only slightly as the frequency of the magnetic field isvaried, while increasing the frequency does results inlonger delay in the response. We stress that the conventional conductivity has the opposite behavior.
We also studied the chiral magnetic wave in the same†∗1∗2

Condensed from the article in Phys. Rev. D 88, 025030(2013)RIKEN Nishina Center
Department of Physics, University of Illinois at Chicago

Abs σσ00.35
0.30
0.250.20
0.15
0.10
0.05

t fm

0.1

0.2

0.3

0.4

0.5

0.1

0.2

0.3

0.4

0.5

t fm

0.020
0.015
0.010
0.005
t fm

Fig. 1. The chiral magnetic conductivity as a functionof thermalization history for frequencies ω = 200MeV(blue solid), ω = 300 MeV(red dashed) and ω =400 MeV(green dotted). The left plot shows the magnitude normalized by chiral magnetic conductivity inequilibrium and the right plot shows the time delay of
the response.

thermalization model for QGP with vanishing axial
charge density. The chiral magnetic wave rises from acoupled fluctuation of the axial and vector charges in
the presence of a background magnetic field. In equilibrium, it has the dispersion ω = ∓vχ k, with the wave
velocity proportional to the magnetic field and the velocity changes sign when the chirality of the charge isreversed2) . We found that the dispersion relation ismodified toω = vout k ∓ ∆ω(k, B).

(2)

We see that the frequency splits into two terms: The
first term is entirely of off-equilibrium origin: the wave
velocity vout vanishes as QGP thermalizes; It is also
independent of the chirality of the charge. The second
term depends on the chirality, and it is linear in bothk and B. It is reminiscent of chiral magnetic wave
velocity in equilibrium. This shows that the physicaleffect of the chiral magnetic wave may be enhanced
owing to the out-of-equilibrium effect.
References
1) D. E. Kharzeev, L. D. McLerran and H. J. Warringa,
Nucl. Phys. A 803, 227 (2008)
2) D. E. Kharzeev and H. -U. Yee, Phys. Rev. D 83, 085007(2011)- 110 -