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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The Rockefeller University & CCNU
with De-fu Hou, Hui Liu
(Fukushima, Kharzeev and Warringa)
In a quark matter of net axial charge
T≠02. RHIC Implementation
i)Excess axial change
Transition between different topologies of QCD
the wind number QCD field strength
Generated by an off-central collision
iii)May provide a new signal of QCD phase transition.
---- 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
＊Beyond thermal equilibrium
under the Infrared limit of
------ Not all Ward identities can be preserved
------ The ones related to gauge symmetries have to be maintained
※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.
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
to all orders and all T and
General tensor structure with Bose symmetry:
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
Anomalous transport coefficients
Son & Surowka
Landsteiner et. al.
Does the anomaly still show up in the regulated