Skip to main content
SpringerLink
Log in

Holographic anomalous conductivities and the chiral magnetic effect

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We calculate anomaly induced conductivities from a holographic gauge theory model using Kubo formulas, making a clear conceptual distinction between thermodynamic state variables such as chemical potentials and external background fields. This allows us to pinpoint ambiguities in previous holographic calculations of the chiral magnetic conductivity. We also calculate the corresponding anomalous current three-point functions in special kinematic regimes. We compare the holographic results to weak coupling calculations using both dimensional regularization and cutoff regularization. In order to reproduce the weak coupling results it is necessary to allow for singular holographic gauge field configurations when a chiral chemical potential is introduced for a chiral charge defined through a gauge invariant but non-conserved chiral density. We argue that this is appropriate for actually addressing charge separation due to the chiral magnetic effect.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D.T. Son and A.R. Zhitnitsky, Quantum anomalies in dense matter, Phys. Rev. D 70 (2004) 074018 [hep-ph/0405216] [SPIRES].

    ADS  Google Scholar 

  2. M.A. Metlitski and A.R. Zhitnitsky, Anomalous axion interactions and topological currents in dense matter, Phys. Rev. D 72 (2005) 045011 [hep-ph/0505072] [SPIRES].

    ADS  Google Scholar 

  3. G.M. Newman and D.T. Son, Response of strongly-interacting matter to magnetic field: Some exact results, Phys. Rev. D 73 (2006) 045006 [hep-ph/0510049] [SPIRES].

    ADS  Google Scholar 

  4. J. Charbonneau and A. Zhitnitsky, Topological Currents in Neutron Stars: Kicks, Precession, Toroidal Fields and Magnetic Helicity, JCAP 08 (2010) 010 [arXiv:0903.4450] [SPIRES].

    ADS  Google Scholar 

  5. D. Kharzeev, Parity violation in hot QCD: Why it can happen and how to look for it, Phys. Lett. B 633 (2006) 260 [hep-ph/0406125] [SPIRES].

    ADS  Google Scholar 

  6. D. Kharzeev and A. Zhitnitsky, Charge separation induced by P-odd bubbles in QCD matter, Nucl. Phys. A 797 (2007) 67 [arXiv:0706.1026] [SPIRES].

    ADS  Google Scholar 

  7. D.E. Kharzeev, L.D. McLerran and H.J. Warringa, The effects of topological charge change in heavy ion collisions: ‘Event by event P and CP-violation’, Nucl. Phys. A 803 (2008) 227 [arXiv:0711.0950] [SPIRES].

    ADS  Google Scholar 

  8. K. Fukushima, D.E. Kharzeev and H.J. Warringa, The Chiral Magnetic Effect, Phys. Rev. D 78 (2008) 074033 [arXiv:0808.3382] [SPIRES].

    ADS  Google Scholar 

  9. D.E. Kharzeev and H.J. Warringa, Chiral Magnetic conductivity, Phys. Rev. D 80 (2009) 034028 [arXiv:0907.5007] [SPIRES].

    ADS  Google Scholar 

  10. A.Y. Alekseev, V.V. Cheianov and J. Fröhlich, Universality of transport properties in equilibrium, Goldstone theorem and chiral anomaly, cond-mat/9803346 [SPIRES].

  11. STAR collaboration, B.I. Abelev et al., Azimuthal Charged-Particle Correlations and Possible Local Strong Parity Violation, Phys. Rev. Lett. 103 (2009) 251601 [arXiv:0909.1739] [SPIRES].

    Article  ADS  Google Scholar 

  12. STAR collaboration, S.A. Voloshin, Probe for the strong parity violation effects at RHIC with three particle correlations, arXiv:0806.0029 [SPIRES].

  13. F. Wang, Effects of Cluster Particle Correlations on Local Parity Violation Observables, Phys. Rev. C 81 (2010) 064902 [arXiv:0911.1482] [SPIRES].

    ADS  Google Scholar 

  14. M. Asakawa, A. Majumder and B. Müller, Electric Charge Separation in Strong Transient Magnetic Fields, Phys. Rev. C 81 (2010) 064912 [arXiv:1003.2436] [SPIRES].

    ADS  Google Scholar 

  15. P.V. Buividovich, M.N. Chernodub, E.V. Luschevskaya and M.I. Polikarpov, Numerical evidence of chiral magnetic effect in lattice gauge theory, Phys. Rev. D 80 (2009) 054503 [arXiv:0907.0494] [SPIRES].

    ADS  Google Scholar 

  16. P.V. Buividovich et al., Magnetic-Field-Induced insulator-conductor transition in SU(2) quenched lattice gauge theory, Phys. Rev. Lett. 105 (2010) 132001 [arXiv:1003.2180] [SPIRES].

    Article  ADS  Google Scholar 

  17. G. Lifschytz and M. Lippert, Anomalous conductivity in holographic QCD, Phys. Rev. D 80 (2009) 066005 [arXiv:0904.4772] [SPIRES].

    ADS  Google Scholar 

  18. H.-U. Yee, Holographic Chiral Magnetic Conductivity, JHEP 11 (2009) 085 [arXiv:0908.4189] [SPIRES].

    Article  ADS  Google Scholar 

  19. A. Rebhan, A. Schmitt and S.A. Stricker, Anomalies and the chiral magnetic effect in the Sakai-Sugimoto model, JHEP 01 (2010) 026 [arXiv:0909.4782] [SPIRES].

    Article  ADS  Google Scholar 

  20. W.A. Bardeen, Anomalous Ward identities in spinor field theories, Phys. Rev. 184 (1969) 1848 [SPIRES].

    Article  ADS  Google Scholar 

  21. C.T. Hill, Anomalies, Chern-Simons terms and chiral delocalization in extra dimensions, Phys. Rev. D 73 (2006) 085001 [hep-th/0601154] [SPIRES].

    ADS  Google Scholar 

  22. H.U. Yee, Holographic Chiral Magnetic Conductivity, Chiral Shear Wave, and Chiral Magnetic Spiral, Talk given at Workshop on P-and CP-odd Effects in Hot and Dense Matter, Brookhaven U.S.A., April 26–30 2010.

  23. T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113 (2005) 843 [hep-th/0412141] [SPIRES].

    Article  ADS  MATH  Google Scholar 

  24. T. Sakai and S. Sugimoto, More on a holographic dual of QCD, Prog. Theor. Phys. 114 (2005) 1083 [hep-th/0507073] [SPIRES].

    Article  ADS  MATH  Google Scholar 

  25. A. Gorsky, P.N. Kopnin and A.V. Zayakin, On the Chiral Magnetic Effect in Soft-Wall AdS/QCD, Phys. Rev. D 83 (2011) 014023 [arXiv:1003.2293] [SPIRES].

    ADS  Google Scholar 

  26. V.A. Rubakov, On chiral magnetic effect and holography, arXiv:1005.1888 [SPIRES].

  27. G.D. Moore and M. Tassler, The Sphaleron Rate in SU(N) Gauge Theory, arXiv:1011.1167 [SPIRES].

  28. K. Ghoroku, M. Ishihara and A. Nakamura, D3/D7 holographic Gauge theory and Chemical potential, Phys. Rev. D 76 (2007) 124006 [arXiv:0708.3706] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  29. S.L. Adler, Axial vector vertex in spinor electrodynamics, Phys. Rev. 177 (1969) 2426 [SPIRES].

    Article  ADS  Google Scholar 

  30. J.S. Bell and R. Jackiw, A PCAC puzzle: π 0 → γγ in the σ-model, Nuovo Cim. A 60 (1969) 47 [SPIRES].

    Article  ADS  Google Scholar 

  31. D.T. Son and A.O. Starinets, Minkowski-space correlators in AdS/CFT correspondence: Recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  32. C.P. Herzog and D.T. Son, Schwinger-Keldysh propagators from AdS/CFT correspondence, JHEP 03 (2003) 046 [hep-th/0212072] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  33. M. Kaminski, K. Landsteiner, J. Mas, J.P. Shock and J. Tarrio, Holographic Operator Mixing and Quasinormal Modes on the Brane, JHEP 02 (2010) 021 [arXiv:0911.3610] [SPIRES].

    Article  ADS  Google Scholar 

  34. N.P. Landsman and C.G. van Weert, Real and Imaginary Time Field Theory at Finite Temperature and Density, Phys. Rept. 145 (1987) 141 [SPIRES].

    Article  ADS  Google Scholar 

  35. T.S. Evans, The Condensed Matter Limit of Relativistic QFT, hep-ph/9510298 [SPIRES].

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, Technische Universität Wien, Wiedner Hauptstrasse 8–10, 1040, Vienna, Austria

    Antti Gynther & Anton Rebhan

  2. Instituto de Física Teórica CSIC-UAM, C-XVI Universidad Autónoma de Madrid, E-28049, Madrid, Spain

    Karl Landsteiner & Francisco Pena-Benitez

Authors
  1. Antti Gynther
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Karl Landsteiner
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Francisco Pena-Benitez
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Anton Rebhan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Antti Gynther.

Additional information

ArXiv ePrint: 1005.2587

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gynther, A., Landsteiner, K., Pena-Benitez, F. et al. Holographic anomalous conductivities and the chiral magnetic effect. J. High Energ. Phys. 2011, 110 (2011). https://doi.org/10.1007/JHEP02(2011)110

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP02(2011)110

Keywords

Search

Navigation