Skip to main content
Log in

Holographic flow of anomalous transport coefficients

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

Abstract

We study the holographic flow of anomalous conductivities induced by gauge and gravitational Chern-Simons terms. We find that the contribution from the gauge Chern-Simons term gives rise to a flow that can be interpreted in terms of an effective, cutoff dependent chemical potential. In contrast the contribution of the gauge-gravitational Chern-Simons term is just the temperature squared and does not flow.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. S.L. Adler, Axial vector vertex in spinor electrodynamics, Phys. Rev. 177 (1969) 2426 .

    Article  ADS  Google Scholar 

  2. J. Bell and R. Jackiw, A PCAC puzzle: π0 → γγ in the σ-model, Nuovo Cim. A 60 (1969) 47 [INSPIRE].

    Article  ADS  Google Scholar 

  3. R. Delbourgo and A. Salam, The gravitational correction to PCAC, Phys. Lett. B 40 (1972) 381 [INSPIRE].

    ADS  Google Scholar 

  4. L. Álvarez-Gaumé and E. Witten, Gravitational anomalies, Nucl. Phys. B 234 (1984) 269 [INSPIRE].

    Article  ADS  Google Scholar 

  5. R.A. Bertlmann, International series of monographs on physics. Vol. 91: Anomalies in quantum field theory, Clarendon, Oxford U.K. (1996), pg. 566.

    Google Scholar 

  6. F. Bastianelli and P. van Nieuwenhuizen, Path integrals and anomalies in curved space, Cambridge University Press, Cambridge U.K. (2006), pg. 379.

    Book  MATH  Google Scholar 

  7. K. Fujikawa and H. Suzuki, Path integrals and quantum anomalies, Clarendon, Oxford U.K. (2004), pg. 284.

    Book  MATH  Google Scholar 

  8. A. Vilenkin, Macroscopic parity violating effects: neutrino fluxes from rotating black holes and in rotating thermal radiation, Phys. Rev. D 20 (1979) 1807 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  9. A. Vilenkin, Quantum field theory at finite temperature in a rotating system, Phys. Rev. D 21 (1980) 2260 [INSPIRE].

    ADS  Google Scholar 

  10. A. Vilenkin, Cancellation of equilibrium parity violating currents, Phys. Rev. D 22 (1980) 3067 [INSPIRE].

    ADS  Google Scholar 

  11. A. Vilenkin, Equilibrium parity violating current in a magnetic field, Phys. Rev. D 22 (1980) 3080 [INSPIRE].

    ADS  Google Scholar 

  12. M. Giovannini and M. Shaposhnikov, Primordial hypermagnetic fields and triangle anomaly, Phys. Rev. D 57 (1998) 2186 [hep-ph/9710234] [INSPIRE].

    ADS  Google Scholar 

  13. A.Y. Alekseev, V.V. Cheianov and J. Fröhlich, Universality of transport properties in equilibrium, Goldstone theorem and chiral anomaly, Phys. Rev. Lett. 81 (1998) 3503 [cond-mat/9803346] [INSPIRE].

    Article  ADS  Google Scholar 

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

    ADS  Google Scholar 

  15. 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] [INSPIRE].

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  17. K. Fukushima, D.E. Kharzeev and H.J. Warringa, The chiral magnetic effect, Phys. Rev. D 78 (2008) 074033 [arXiv:0808.3382] [INSPIRE].

    ADS  Google Scholar 

  18. J. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  19. N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Dutta, R. Loganayagam, et al., Hydrodynamics from charged black branes, JHEP 01 (2011) 094 [arXiv:0809.2596] [INSPIRE].

    Article  ADS  Google Scholar 

  20. D.T. Son and P. Surowka, Hydrodynamics with triangle anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  21. T. Kalaydzhyan and I. Kirsch, Fluid/gravity model for the chiral magnetic effect, Phys. Rev. Lett. 106 (2011) 211601 [arXiv:1102.4334] [INSPIRE].

    Article  ADS  Google Scholar 

  22. A. Sadofyev and M. Isachenkov, The Chiral magnetic effect in hydrodynamical approach, Phys. Lett. B 697 (2011) 404 [arXiv:1010.1550] [INSPIRE].

    ADS  Google Scholar 

  23. K. Landsteiner, E. Megías and F. Pena-Benitez, Gravitational anomaly and transport, Phys. Rev. Lett. 107 (2011) 021601 [arXiv:1103.5006] [INSPIRE].

    Article  ADS  Google Scholar 

  24. K. Landsteiner, E. Megías, L. Melgar and F. Pena-Benitez, Holographic gravitational anomaly and chiral vortical effect, JHEP 09 (2011) 121 [arXiv:1107.0368] [INSPIRE].

    Article  ADS  Google Scholar 

  25. I. Amado, K. Landsteiner and F. Pena-Benitez, Anomalous transport coefficients from Kubo formulas in Holography, JHEP 05 (2011) 081 [arXiv:1102.4577] [INSPIRE].

    Article  ADS  Google Scholar 

  26. R. Loganayagam and P. Surowka, Anomaly/Transport in an Ideal Weyl gas, JHEP 04 (2012) 097 [arXiv:1201.2812] [INSPIRE].

    Article  ADS  Google Scholar 

  27. S. Chapman, Y. Neiman and Y. Oz, Fluid/Gravity Correspondence, Local Wald Entropy Current and Gravitational Anomaly, JHEP 07 (2012) 128 [arXiv:1202.2469] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. V. Balasubramanian and P. Kraus, Space-time and the holographic renormalization group, Phys. Rev. Lett. 83 (1999) 3605 [hep-th/9903190] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  29. J. de Boer, E.P. Verlinde and H.L. Verlinde, On the holographic renormalization group, JHEP 08 (2000) 003 [hep-th/9912012] [INSPIRE].

    Article  Google Scholar 

  30. N. Iqbal and H. Liu, Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm, Phys. Rev. D 79 (2009) 025023 [arXiv:0809.3808] [INSPIRE].

    ADS  Google Scholar 

  31. G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics, JHEP 09 (2002) 043 [hep-th/0205052] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  32. P. Kovtun, D.T. Son and A.O. Starinets, Holography and hydrodynamics: diffusion on stretched horizons, JHEP 10 (2003) 064 [hep-th/0309213] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  33. Y. Matsuo, S.-J. Sin and Y. Zhou, Mixed RG Flows and Hydrodynamics at Finite Holographic Screen, JHEP 01 (2012) 130 [arXiv:1109.2698] [INSPIRE].

    Article  ADS  Google Scholar 

  34. B.-H. Lee, S.S. Pal and S.-J. Sin, RG flow of transport quantities, Int. J. Mod. Phys. A 27 (2012) 1250071 [arXiv:1108.5577] [INSPIRE].

    ADS  Google Scholar 

  35. X.-H. Ge, Y. Ling, Y. Tian and X.-N. Wu, Holographic RG flows and transport coefficients in Einstein-Gauss-Bonnet-Maxwell theory, JHEP 01 (2012) 117 [arXiv:1112.0627] [INSPIRE].

    Article  ADS  Google Scholar 

  36. T. Faulkner, H. Liu and M. Rangamani, Integrating out geometry: holographic Wilsonian RG and the membrane paradigm, JHEP 08 (2011) 051 [arXiv:1010.4036] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  37. I. Heemskerk and J. Polchinski, Holographic and Wilsonian renormalization groups, JHEP 06 (2011) 031 [arXiv:1010.1264] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  38. I. Bredberg, C. Keeler, V. Lysov and A. Strominger, Wilsonian approach to fluid/gravity duality, JHEP 03 (2011) 141 [arXiv:1006.1902] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  39. S. Grozdanov, Wilsonian renormalisation and the exact cut-off scale from holographic duality, JHEP 06 (2012) 079 [arXiv:1112.3356] [INSPIRE].

    Article  ADS  Google Scholar 

  40. S.-J. Sin and Y. Zhou, Holographic Wilsonian RG flow and sliding membrane paradigm, JHEP 05 (2011) 030 [arXiv:1102.4477] [INSPIRE].

    Article  ADS  Google Scholar 

  41. D.E. Kharzeev and H.J. Warringa, Chiral magnetic conductivity, Phys. Rev. D 80 (2009) 034028 [arXiv:0907.5007] [INSPIRE].

    ADS  Google Scholar 

  42. H.-U. Yee, Holographic chiral magnetic conductivity, JHEP 11 (2009) 085 [arXiv:0908.4189] [INSPIRE].

    Article  ADS  Google Scholar 

  43. 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] [INSPIRE].

    Article  ADS  Google Scholar 

  44. A. Gynther, K. Landsteiner, F. Pena-Benitez and A. Rebhan, Holographic anomalous conductivities and the chiral magnetic effect, JHEP 02 (2011) 110 [arXiv:1005.2587] [INSPIRE].

    Article  ADS  Google Scholar 

  45. L. Melgar, I. Papadimitriou and F. Pena-Benitez, Non-perturbative holographic analsysis of gravitational anomalies, in preparation.

  46. S. Alexander and N. Yunes, Chern-Simons modified general relativity, Phys. Rept. 480 (2009) 1 [arXiv:0907.2562] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  47. 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] [INSPIRE].

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Karl Landsteiner.

Additional information

ArXiv ePrint: 1206.4440

Rights and permissions

Reprints and permissions

About this article

Cite this article

Landsteiner, K., Melgar, L. Holographic flow of anomalous transport coefficients. J. High Energ. Phys. 2012, 131 (2012). https://doi.org/10.1007/JHEP10(2012)131

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP10(2012)131

Keywords

Navigation