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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. 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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  1. 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

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

  3. 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

  4. 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

  5. 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

  6. 3. The robustness of under the Infrared limit of i.e.

  7. 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.

  8. 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:

  9. Ward identities post regularization:

  10. 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.

  11. III General properties of CME i) Naïve axial charge & conserved axial charge should be used in thermodynamics equilibrium(Rubakov)

  12. ii) Grand partition function: iii) Linear response The usual photon self-energy tensor, subject to higher order corrections

  13. iv)The Taylor expansion in Chiral magnetic current Normal term Anomaly term

  14. The limit to all orders and all T and

  15. The limit General tensor structure with Bose symmetry:

  16. The electromagnetic gauge invariance: If the infrared limit exists: to all orders

  17. III. One loop calculation Continuation of imaginary Matsubara to with real for retarded (advanced) response function after the summation over Matsubara

  18. Subtlety of IR limit: Kharzeev & Warringar IR singularity: IR singularity:

  19. III. Summary

  20. Current project Anomalous transport coefficients Son & Surowka Landsteiner et. al.

  21. Anomaly and thermodynamics Does the anomaly still show up in the regulated ?

  22. Thank you!

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