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. The contents. An introduction of CME Axial anomaly in QCD General properties of CME One loop calculation Summary

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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


The contents

  • An introduction of CME

  • Axial anomaly in QCD

  • General properties of CME

  • One loop calculation

  • Summary

  • Current project


I. An introduction to CME

1. A charged massless quark in a magnetic field

(Fukushima, Kharzeev and Warringa)

In a quark matter of net axial charge

Color-flavor factor


T=0

T≠0

2. RHIC Implementation

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


III. One loop calculation

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:


III. Summary


Current project

Anomalous transport coefficients

Son & Surowka

Landsteiner et. al.


Anomaly and thermodynamics

Does the anomaly still show up in the regulated

?


Thank you!


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