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Holographic gravitational anomaly and chiral vortical effect

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Abstract

We analyze a holographic model with a pure gauge and a mixed gauge-gravitational Chern-Simons term in the action. These are the holographic implementations of the usual chiral and the mixed gauge-gravitational anomalies in four dimensional field theories with chiral fermions. We discuss the holographic renormalization and show that the gauge-gravitational Chern-Simons term does not induce new divergences. In order to cancel contributions from the extrinsic curvature at a boundary at finite distance a new type of counterterm has to be added however. This counterterm can also serve to make the Dirichlet problem well defined in case the gauge field strength vanishes on the boundary. A charged asymptotically AdS black hole is a solution to the theory and as an application we compute the chiral magnetic and chiral vortical conductivities via Kubo formulas. We find that the characteristic term proportional to T 2 is present also at strong coupling and that its numerical value is not renormalized compared to the weak coupling result.

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References

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

    Article  ADS  Google Scholar 

  2. 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 

  3. R. Delbourgo and A. Salam, The gravitational correction to pcac, Phys. Lett. B 40 (1972) 381. [Phys.Lett.B40:381–382,1972], PHLTA,B40,381;

    ADS  Google Scholar 

  4. T. Eguchi and P.G.O. Freund, Quantum gravity and world topology, Phys. Rev. Lett. 37 (1976) 1251 [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  6. 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 

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

    Article  ADS  MathSciNet  Google Scholar 

  8. N. Banerjee et al., Hydrodynamics from charged black branes, JHEP 01 (2011) 094 [arXiv:0809.2596] [SPIRES].

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  10. A. Vilenkin, Parity nonconservation and neutrino transport in magnetic fields, Astrophys. J. 451 (1995) 700 [SPIRES].

    Article  ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  13. A. Vilenkin, Parity violating currents in thermal radiation, Phys. Lett. B 80 (1978) 150 [SPIRES].

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

  16. 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 

  17. G.M. Newman, Anomalous hydrodynamics, JHEP 01 (2006) 158 [hep-ph/0511236] [SPIRES].

    Article  ADS  Google Scholar 

  18. 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 

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

    Article  ADS  Google Scholar 

  20. M. Torabian and H.-U. Yee, Holographic nonlinear hydrodynamics from AdS/CFT with multiple/non-abelian symmetries, JHEP 08 (2009) 020 [arXiv:0903.4894] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  21. 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 

  22. L. Brits and J. Charbonneau, A constraint-based approach to the chiral magnetic effect, Phys. Rev. D 83 (2011) 126013 [arXiv:1009.4230] [SPIRES].

    ADS  Google Scholar 

  23. 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] [SPIRES].

    Article  ADS  Google Scholar 

  24. 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 

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

    Article  ADS  Google Scholar 

  26. C. Hoyos, T. Nishioka and A. O’Bannon, A chiral magnetic effect from AdS/CFT with flavor, arXiv:1106.4030 [SPIRES].

  27. C. Eling, Y. Neiman and Y. Oz, Holographic non-abelian charged hydrodynamics from the dynamics of null horizons, JHEP 12 (2010) 086 [arXiv:1010.1290] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  28. 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 

  29. M. Abramczyk, T. Blum, G. Petropoulos and R. Zhou, Chiral magnetic effect in 2 + 1 flavor QCD + QED, PoS(LAT2009)181 [arXiv:0911.1348] [SPIRES].

  30. A. Yamamoto, Chiral magnetic effect in lattice QCD with a chiral chemical potential, Phys. Rev. Lett. 107 (2011) 031601 [arXiv:1105.0385] [SPIRES].

    Article  ADS  Google Scholar 

  31. 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 

  32. D.E. Kharzeev and H.-U. Yee, Chiral magnetic wave, Phys. Rev. D 83 (2011) 085007 [arXiv:1012.6026] [SPIRES].

    ADS  Google Scholar 

  33. D.E. Kharzeev and D.T. Son, Testing the chiral magnetic and chiral vortical effects in heavy ion collisions, Phys. Rev. Lett. 106 (2011) 062301 [arXiv:1010.0038] [SPIRES].

    Article  ADS  Google Scholar 

  34. B. Keren-Zur and Y. Oz, Hydrodynamics and the detection of the QCD axial anomaly in heavy ion collisions, JHEP 06 (2010) 006 [arXiv:1002.0804] [SPIRES].

    Article  ADS  Google Scholar 

  35. 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 

  36. N.N. Ajitanand, R.A. Lacey, A. Taranenko and J.M. Alexander, A new method for the experimental study of topological effects in the quark-gluon plasma, Phys. Rev. C 83 (2011) 011901 [arXiv:1009.5624] [SPIRES].

    ADS  Google Scholar 

  37. 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 

  38. STAR collaboration, B.I. Abelev et al., Observation of charge-dependent azimuthal correlations and possible local strong parity violation in heavy ion collisions, Phys. Rev. C 81 (2010) 054908 [arXiv:0909.1717] [SPIRES].

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  40. D. Hou, H. Liu and H.-c. Ren, Some field theoretic issues regarding the chiral magnetic effect, JHEP 05 (2011) 046 [arXiv:1103.2035] [SPIRES].

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  42. M. Le Bellac, Equilibrium and non-equilibrium statistical thermodynamics, Cambridge University Press, Cambridge U.K. (2006).

    Google Scholar 

  43. D.E. Kharzeev and H.-U. Yee, Anomalies and time reversal invariance in relativistic hydrodynamics: the second order and higher dimensional formulations, arXiv:1105.6360 [SPIRES].

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

    Article  ADS  Google Scholar 

  45. A.V. Sadofyev and M.V. Isachenkov, The chiral magnetic effect in hydrodynamical approach, Phys. Lett. B 697 (2011) 404 [arXiv:1010.1550] [SPIRES].

    ADS  Google Scholar 

  46. Y. Neiman and Y. Oz, Relativistic hydrodynamics with general anomalous charges, JHEP 03 (2011) 023 [arXiv:1011.5107] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  47. J. Bhattacharya, S. Bhattacharyya, S. Minwalla and A. Yarom, A theory of first order dissipative superfluid dynamics, arXiv:1105.3733 [SPIRES].

  48. S. Lin, On the anomalous superfluid hydrodynamics, arXiv:1104.5245 [SPIRES].

  49. Y. Neiman and Y. Oz, Anomalies in superfluids and a chiral electric effect, JHEP 09 (2011) 011 [arXiv:1106.3576] [SPIRES].

    Article  ADS  Google Scholar 

  50. R. Loganayagam, Anomaly induced transport in arbitrary dimensions, arXiv:1106.0277 [SPIRES].

  51. J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [SPIRES].

    Article  MATH  MathSciNet  Google Scholar 

  52. S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  53. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].

    MATH  MathSciNet  Google Scholar 

  54. O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  55. O. Andreev and V.I. Zakharov, Heavy-quark potentials and AdS/QCD, Phys. Rev. D 74 (2006) 025023 [hep-ph/0604204] [SPIRES].

    ADS  Google Scholar 

  56. B. Galow, E. Megias, J. Nian and H.J. Pirner, Phenomenology of AdS/QCD and its gravity dual, Nucl. Phys. B 834 (2010) 330 [arXiv:0911.0627] [SPIRES].

    Article  ADS  Google Scholar 

  57. U. Gürsoy, E. Kiritsis, L. Mazzanti and F. Nitti, Holography and thermodynamics of 5D dilaton-gravity, JHEP 05 (2009) 033 [arXiv:0812.0792] [SPIRES].

    Article  Google Scholar 

  58. E. Megias, H.J. Pirner and K. Veschgini, QCD-thermodynamics using 5-dim gravity, Phys. Rev. D 83 (2011) 056003 [arXiv:1009.2953] [SPIRES].

    ADS  Google Scholar 

  59. K. Veschgini, E. Megias and H.J. Pirner, Trouble finding the optimal AdS/QCD, Phys. Lett. B 696 (2011) 495 [arXiv:1009.4639] [SPIRES].

    ADS  Google Scholar 

  60. R. Jackiw and S.Y. Pi, Chern-Simons modification of general relativity, Phys. Rev. D 68 (2003) 104012 [gr-qc/0308071] [SPIRES].

    ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  62. O. Saremi and D.T. Son, Hall viscosity from gauge/gravity duality, arXiv:1103.4851 [SPIRES].

  63. T. Delsate, V. Cardoso and P. Pani, Anti de Sitter black holes and branes in dynamical Chern-Simons gravity: perturbations, stability and the hydrodynamic modes, JHEP 06 (2011) 055 [arXiv:1103.5756] [SPIRES].

    Article  ADS  Google Scholar 

  64. R.A. Bertlmann, Anomalies in quantum field theory, Clarendon Press, Oxford U.K. (1996).

    MATH  Google Scholar 

  65. D. Martelli and W. Mueck, Holographic renormalization and Ward identities with the Hamilton-Jacobi method, Nucl. Phys. B 654 (2003) 248 [hep-th/0205061] [SPIRES].

    Article  ADS  Google Scholar 

  66. I. Papadimitriou and K. Skenderis, AdS/CFT correspondence and geometry, hep-th/0404176 [SPIRES].

  67. H.-U. Yee and I. Zahed, Holographic two dimensional QCD and Chern-Simons term, JHEP 07 (2011) 033 [arXiv:1103.6286] [SPIRES].

    Article  ADS  Google Scholar 

  68. P. Kraus and F. Larsen, Holographic gravitational anomalies, JHEP 01 (2006) 022 [hep-th/0508218] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  69. D. Grumiller, R.B. Mann and R. McNees, Dirichlet boundary value problem for Chern-Simons modified gravity, Phys. Rev. D 78 (2008) 081502 [arXiv:0803.1485] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  70. T.E. Clark, S.T. Love and T. ter Veldhuis, Holographic currents and Chern-Simons terms, Phys. Rev. D 82 (2010) 106004 [arXiv:1006.2400] [SPIRES].

    ADS  Google Scholar 

  71. 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  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  73. 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 

  74. I. Amado, M. Kaminski and K. Landsteiner, Hydrodynamics of holographic superconductors, JHEP 05 (2009) 021 [arXiv:0903.2209] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  75. L. Bonora, M. Cvitan, P.D. Prester, S. Pallua and I. Smolic, Gravitational Chern-Simons lagrangian terms and spherically symmetric spacetimes, arXiv:1105.4792 [SPIRES].

  76. S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear fluid dynamics from gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [SPIRES].

    Article  ADS  Google Scholar 

  77. K. Landsteiner, E. Megias and F. Pena-Benitez, Fluid/gravity and Chern Simons terms, work in progress.

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  1. Instituto de Física Teórica UAM/CSIC, C/ Nicolás Cabrera 13-15, Universidad Autónoma de Madrid, Cantoblanco, 28049, Madrid, Spain

    Karl Landsteiner, Eugenio Megías, Luis Melgar & Francisco Pena-Benitez

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  1. Karl Landsteiner
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  2. Eugenio Megías
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Correspondence to Eugenio Megías.

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ArXiv ePrint: 1107.0368

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Landsteiner, K., Megías, E., Melgar, L. et al. Holographic gravitational anomaly and chiral vortical effect. J. High Energ. Phys. 2011, 121 (2011). https://doi.org/10.1007/JHEP09(2011)121

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