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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Some field theoretical issues of the chiral magnetic effect

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

The contents

  • An introduction of CME

  • Axial anomaly in QCD

  • General properties of CME

  • One loop calculation

  • Summary

  • Current project


1 a charged massless quark in a magnetic field

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


2 rhic implementation

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


Some field theoretical issues of the chiral magnetic effect

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


Some field theoretical issues of the chiral magnetic effect

3. The robustness of

under the Infrared limit of

i.e.


Some field theoretical issues of the chiral magnetic effect

  • 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.


Some field theoretical issues of the chiral magnetic effect

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:


Some field theoretical issues of the chiral magnetic effect

  • Ward identities post regularization:


Some field theoretical issues of the chiral magnetic effect

  • 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.


Some field theoretical issues of the chiral magnetic effect

III General properties of CME

i) Naïve axial charge & conserved axial charge

should be used in thermodynamics equilibrium(Rubakov)


Some field theoretical issues of the chiral magnetic effect

ii) Grand partition function:

iii) Linear response

The usual photon self-energy tensor, subject to

higher order corrections


Some field theoretical issues of the chiral magnetic effect

iv)The Taylor expansion in

Chiral magnetic current

Normal term

Anomaly term


Some field theoretical issues of the chiral magnetic effect

The limit

to all orders and all T and


Some field theoretical issues of the chiral magnetic effect

The limit

General tensor structure with Bose symmetry:


Some field theoretical issues of the chiral magnetic effect

The electromagnetic gauge invariance:

If the infrared limit exists:

to all orders


Iii one loop calculation

III. One loop calculation

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


Some field theoretical issues of the chiral magnetic effect

Subtlety of IR limit:

Kharzeev

& Warringar

IR singularity:

IR singularity:


Iii summary

III. Summary


Some field theoretical issues of the chiral magnetic effect

Current project

Anomalous transport coefficients

Son & Surowka

Landsteiner et. al.


Some field theoretical issues of the chiral magnetic effect

Anomaly and thermodynamics

Does the anomaly still show up in the regulated

?


Some field theoretical issues of the chiral magnetic effect

Thank you!


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