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Some Field Theoretical Issues of the Chiral Magnetic Effect

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CPODD 2012, BNL

Some Field Theoretical Issues of the Chiral Magnetic Effect

Hai-cang Ren

The Rockefeller University & CCNU

with De-fu Hou, Hui Liu

JHEP 05(2011)046

- An introduction of CME
- Axial anomaly in QCD
- General properties of CME
- One loop calculation
- Summary
- Current project

I. An introduction to CME

(Fukushima, Kharzeev and Warringa)

In a quark matter of net axial charge

Color-flavor factor

T=0

T≠0

i)Excess axial change

Transition between different topologies of QCD

Axial anomaly

the wind number QCD field strength

ii)Magnetic field

Generated by an off-central collision

ion

ion

iii)May provide a new signal of QCD phase transition.

iv)Theoretical approach:

---- Field theory (Fukushima et. al., Kharzeev et. al.)

---- Holographic theory(Yee, Rebhan et. al.)

v)There are experimental evidences, remains to be solidified.

vi)Complication in RHIC:

＊Inhomogeneous & time dependent magnetic field

＊Inhomogeneous temperature and chemical potentials

local equilibrium

＊Beyond thermal equilibrium

3. The robustness of

under the Infrared limit of

i.e.

- A relativistic quantum field theory at nonzero temperature
- and/or chemical potentials
- UV divergence is no worse than vacuum
- IR is more problematic because:
- ---- The appearance of the ratio
- ---- The appearance of the ratios etc.
- ---- Linde’s problem with gluons.

II. Axial anomaly in QCD

- Naïve Ward identities:

- UV divergence demands regularization (e.g. Pauli Villars)
------ Not all Ward identities can be preserved

------ The ones related to gauge symmetries have to be maintained

PV regulators:

- Ward identities post regularization:

- Applications of the axial anomaly:

※The explanation of the rate of

※ The solution of UA(1) problem

※ Link the change of the axial charge and the change of topology.

※Chiral magnetic effect, chiral vortical effect, etc.

III General properties of CME

i) Naïve axial charge & conserved axial charge

should be used in thermodynamics equilibrium(Rubakov)

ii) Grand partition function:

iii) Linear response

The usual photon self-energy tensor, subject to

higher order corrections

iv)The Taylor expansion in

Chiral magnetic current

Normal term

Anomaly term

The limit

to all orders and all T and

The limit

General tensor structure with Bose symmetry:

The electromagnetic gauge invariance:

If the infrared limit exists:

to all orders

Continuation of imaginary Matsubara to with real for retarded (advanced) response function after the summation over Matsubara

Subtlety of IR limit:

Kharzeev

& Warringar

IR singularity:

IR singularity:

Current project

Anomalous transport coefficients

Son & Surowka

Landsteiner et. al.

Anomaly and thermodynamics

Does the anomaly still show up in the regulated

?

Thank you!