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Fluctuations and instabilities of a holographic metal

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Abstract

We analyze the quasinormal modes of the D2-D8’ model of 2+1-dimensional, strongly-coupled, charged fermions in a background magnetic field and at non-zero density. The model is known to include a quantum Hall phase with integer filling fraction. As expected, we find a hydrodynamical diffusion mode at small momentum and the nonzero-temperature holographic zero sound, which becomes massive above a critical magnetic field. We confirm the previously-known thermodynamic instability. In addition, we discover an instability at low temperature, large mass, and in a charge density and magnetic field range near the quantum Hall phase to an inhomogeneous striped phase.

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References

  1. A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  2. O. Bergman, N. Jokela, G. Lifschytz and M. Lippert, Quantum Hall Effect in a Holographic Model, JHEP 10 (2010) 063 [arXiv:1003.4965] [INSPIRE].

    Article  ADS  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  4. A. Karch and L. Randall, Localized gravity in string theory, Phys. Rev. Lett. 87 (2001) 061601 [hep-th/0105108] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  5. A. Karch and L. Randall, Open and closed string interpretation of SUSY CFT’s on branes with boundaries, JHEP 06 (2001) 063 [hep-th/0105132] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. O. DeWolfe, D.Z. Freedman and H. Ooguri, Holography and defect conformal field theories, Phys. Rev. D 66 (2002) 025009 [hep-th/0111135] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  7. N.R. Constable, J. Erdmenger, Z. Guralnik and I. Kirsch, Intersecting D-3 branes and holography, Phys. Rev. D 68 (2003) 106007 [hep-th/0211222] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  8. T. Sakai and J. Sonnenschein, Probing flavored mesons of confining gauge theories by supergravity, JHEP 09 (2003) 047 [hep-th/0305049] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. J. Babington, J. Erdmenger, N.J. Evans, Z. Guralnik and I. Kirsch, Chiral symmetry breaking and pions in nonsupersymmetric gauge/gravity duals, Phys. Rev. D 69 (2004) 066007 [hep-th/0306018] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  10. P. Ouyang, Holomorphic D7 branes and flavored N = 1 gauge theories, Nucl. Phys. B 699 (2004) 207 [hep-th/0311084] [INSPIRE].

    Article  ADS  Google Scholar 

  11. M. Kruczenski, D. Mateos, R.C. Myers and D.J. Winters, Towards a holographic dual of large-N c QCD, JHEP 05 (2004) 041 [hep-th/0311270] [INSPIRE].

    Article  ADS  Google Scholar 

  12. M. Van Raamsdonk and K. Whyte, Baryon charge from embedding topology and a continuous meson spectrum in a new holographic gauge theory, JHEP 05 (2010) 073 [arXiv:0912.0752] [INSPIRE].

    Article  Google Scholar 

  13. D.K. Hong and H.-U. Yee, Holographic aspects of three dimensional QCD from string theory, JHEP 05 (2010) 036 [Erratum ibid. 1008 (2010) 120] [arXiv:1003.1306] [INSPIRE].

  14. S.S. Pal, Quantum phase transition in a Dp-Dq system, Phys. Rev. D 82 (2010) 086013 [arXiv:1006.2444] [INSPIRE].

    ADS  Google Scholar 

  15. K. Jensen, More Holographic Berezinskii-Kosterlitz-Thouless Transitions, Phys. Rev. D 82 (2010) 046005 [arXiv:1006.3066] [INSPIRE].

    ADS  Google Scholar 

  16. E. Conde and A.V. Ramallo, On the gravity dual of Chern-Simons-matter theories with unquenched flavor, JHEP 07 (2011) 099 [arXiv:1105.6045] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  17. G. Zafrir, Embedding massive flavor in ABJM, JHEP 10 (2012) 056 [arXiv:1202.4295] [INSPIRE].

    Article  ADS  Google Scholar 

  18. S.K. Domokos, C. Hoyos and J. Sonnenschein, Holographic Josephson Junctions and Berry holonomy from D-branes, JHEP 10 (2012) 073 [arXiv:1207.2182] [INSPIRE].

    Article  ADS  Google Scholar 

  19. N. Jokela, J. Mas, A.V. Ramallo and D. Zoakos, Thermodynamics of the brane in Chern-Simons matter theories with flavor, arXiv:1211.0630 [INSPIRE].

  20. S. Sachdev, Holographic metals and the fractionalized Fermi liquid, Phys. Rev. Lett. 105 (2010) 151602 [arXiv:1006.3794] [INSPIRE].

    Article  ADS  Google Scholar 

  21. L. Huijse and S. Sachdev, Fermi surfaces and gauge-gravity duality, Phys. Rev. D 84 (2011) 026001 [arXiv:1104.5022] [INSPIRE].

    ADS  Google Scholar 

  22. M. Ammon, J. Erdmenger, S. Lin, S. Muller, A. O’Bannon and J. P. Shock, On Stability and Transport of Cold Holographic Matter, JHEP 09 (2011) 030 [arXiv:1108.1798] [INSPIRE].

    Article  ADS  Google Scholar 

  23. A. Karch, D. Son and A. Starinets, Zero Sound from Holography, arXiv:0806.3796 [INSPIRE].

  24. M. Kulaxizi and A. Parnachev, Comments on Fermi Liquid from Holography, Phys. Rev. D 78 (2008) 086004 [arXiv:0808.3953] [INSPIRE].

    ADS  Google Scholar 

  25. M. Goykhman, A. Parnachev and J. Zaanen, Fluctuations in finite density holographic quantum liquids, JHEP 10 (2012) 045 [arXiv:1204.6232] [INSPIRE].

    Article  ADS  Google Scholar 

  26. D.K. Brattan, R.A. Davison, S.A. Gentle and A. O’Bannon, Collective Excitations of Holographic Quantum Liquids in a Magnetic Field, JHEP 11 (2012) 084 [arXiv:1209.0009] [INSPIRE].

    Article  ADS  Google Scholar 

  27. V. Puletti, S. Nowling, L. Thorlacius and T. Zingg, Friedel Oscillations in Holographic Metals, JHEP 01 (2012) 073 [arXiv:1110.4601] [INSPIRE].

    Article  ADS  Google Scholar 

  28. M. Blake, S. Bolognesi, D. Tong and K. Wong, Holographic Dual of the Lowest Landau Level, JHEP 12 (2012) 039 [arXiv:1208.5771] [INSPIRE].

    Article  ADS  Google Scholar 

  29. N. Jokela, M. Jarvinen and M. Lippert, A holographic quantum Hall model at integer filling, JHEP 05 (2011) 101 [arXiv:1101.3329] [INSPIRE].

    Article  ADS  Google Scholar 

  30. J.H. Brodie, L. Susskind and N. Toumbas, How Bob Laughlin tamed the giant graviton from Taub-NUT space, JHEP 02 (2001) 003 [hep-th/0010105] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  31. O. Bergman, Y. Okawa and J.H. Brodie, The Stringy quantum Hall fluid, JHEP 11 (2001) 019 [hep-th/0107178] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  32. S. Hellerman and L. Susskind, Realizing the quantum Hall system in string theory, hep-th/0107200 [INSPIRE].

  33. E. Keski-Vakkuri and P. Kraus, Quantum Hall Effect in AdS/CFT, JHEP 09 (2008) 130 [arXiv:0805.4643] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  34. J.L. Davis, P. Kraus and A. Shah, Gravity Dual of a Quantum Hall Plateau Transition, JHEP 11 (2008) 020 [arXiv:0809.1876] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  35. J. Alanen, E. Keski-Vakkuri, P. Kraus and V. Suur-Uski, AC Transport at Holographic Quantum Hall Transitions, JHEP 11 (2009) 014 [arXiv:0905.4538] [INSPIRE].

    Article  ADS  Google Scholar 

  36. S.-J. Rey, String theory on thin semiconductors: Holographic realization of Fermi points and surfaces, Prog. Theor. Phys. Suppl. 177 (2009) 128 [arXiv:0911.5295] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  37. R.C. Myers and M.C. Wapler, Transport Properties of Holographic Defects, JHEP 12 (2008) 115 [arXiv:0811.0480] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  38. X. Dong, S. Harrison, S. Kachru, G. Torroba and H. Wang, Aspects of holography for theories with hyperscaling violation, JHEP 06 (2012) 041 [arXiv:1201.1905] [INSPIRE].

    Article  ADS  Google Scholar 

  39. M. Ammon, M. Kaminski and A. Karch, Hyperscaling-Violation on Probe D-branes, JHEP 11 (2012) 028 [arXiv:1207.1726] [INSPIRE].

    Article  ADS  Google Scholar 

  40. I. Kanitscheider, K. Skenderis and M. Taylor, Precision holography for non-conformal branes, JHEP 09 (2008) 094 [arXiv:0807.3324] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  41. N. Jokela, M. Jarvinen and M. Lippert, Fluctuations of a holographic quantum Hall fluid, JHEP 01 (2012) 072 [arXiv:1107.3836] [INSPIRE].

    Article  ADS  Google Scholar 

  42. K.-Y. Kim and I. Zahed, Baryonic Response of Dense Holographic QCD, JHEP 12 (2008) 075 [arXiv:0811.0184] [INSPIRE].

    Article  ADS  Google Scholar 

  43. 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 

  44. O. Bergman, N. Jokela, G. Lifschytz and M. Lippert, Striped instability of a holographic Fermi-like liquid, JHEP 10 (2011) 034 [arXiv:1106.3883] [INSPIRE].

    Article  ADS  Google Scholar 

  45. N. Jokela, G. Lifschytz and M. Lippert, Magnetic effects in a holographic Fermi-like liquid, JHEP 05 (2012) 105 [arXiv:1204.3914] [INSPIRE].

    Article  ADS  Google Scholar 

  46. R.A. Davison and A.O. Starinets, Holographic zero sound at finite temperature, Phys. Rev. D 85 (2012) 026004 [arXiv:1109.6343] [INSPIRE].

    ADS  Google Scholar 

  47. A. Gorsky and A. Zayakin, Anomalous Zero Sound, arXiv:1206.4725 [INSPIRE].

  48. S. Nakamura, H. Ooguri and C.-S. Park, Gravity Dual of Spatially Modulated Phase, Phys. Rev. D 81 (2010) 044018 [arXiv:0911.0679] [INSPIRE].

    ADS  Google Scholar 

  49. H. Ooguri and C.-S. Park, Holographic End-Point of Spatially Modulated Phase Transition, Phys. Rev. D 82 (2010) 126001 [arXiv:1007.3737] [INSPIRE].

    ADS  Google Scholar 

  50. H. Ooguri and C.-S. Park, Spatially Modulated Phase in Holographic quark-gluon Plasma, Phys. Rev. Lett. 106 (2011) 061601 [arXiv:1011.4144] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  51. C.B. Bayona, K. Peeters and M. Zamaklar, A Non-homogeneous ground state of the low-temperature Sakai-Sugimoto model, JHEP 06 (2011) 092 [arXiv:1104.2291] [INSPIRE].

    Article  ADS  Google Scholar 

  52. A. Donos and J.P. Gauntlett, Holographic striped phases, JHEP 08 (2011) 140 [arXiv:1106.2004] [INSPIRE].

    Article  ADS  Google Scholar 

  53. A. Donos, J.P. Gauntlett and C. Pantelidou, Spatially modulated instabilities of magnetic black branes, JHEP 01 (2012) 061 [arXiv:1109.0471] [INSPIRE].

    Article  ADS  Google Scholar 

  54. A. Donos and J.P. Gauntlett, Holographic helical superconductors, JHEP 12 (2011) 091 [arXiv:1109.3866] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  55. H. Ooguri and M. Oshikawa, Instability in magnetic materials with dynamical axion field, Phys. Rev. Lett. 108 (2012) 161803 [arXiv:1112.1414] [INSPIRE].

    Article  ADS  Google Scholar 

  56. A. Donos, J.P. Gauntlett and C. Pantelidou, Magnetic and Electric AdS Solutions in String- and M-theory, Class. Quant. Grav. 29 (2012) 194006 [arXiv:1112.4195] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  57. A. Ballon-Bayona, K. Peeters and M. Zamaklar, A chiral magnetic spiral in the holographic Sakai-Sugimoto model, JHEP 11 (2012) 164 [arXiv:1209.1953] [INSPIRE].

    Article  ADS  Google Scholar 

  58. O. Bergman, J. Erdmenger and G. Lifschytz, A Review of Magnetic Phenomena in Probe-Brane Holographic Matter, arXiv:1207.5953 [INSPIRE].

  59. N. Itzhaki, J.M. Maldacena, J. Sonnenschein and S. Yankielowicz, Supergravity and the large-N limit of theories with sixteen supercharges, Phys. Rev. D 58 (1998) 046004 [hep-th/9802042] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  60. A. Karch and A. O’Bannon, Metallic AdS/CFT, JHEP 09 (2007) 024 [arXiv:0705.3870] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  61. A. O’Bannon, Hall Conductivity of Flavor Fields from AdS/CFT, Phys. Rev. D 76 (2007) 086007 [arXiv:0708.1994] [INSPIRE].

    ADS  Google Scholar 

  62. K.-Y. Kim and D.-W. Pang, Holographic DC conductivities from the open string metric, JHEP 09 (2011) 051 [arXiv:1108.3791] [INSPIRE].

    Article  ADS  Google Scholar 

  63. A. Karch, M. Kulaxizi and A. Parnachev, Notes on Properties of Holographic Matter, JHEP 11 (2009) 017 [arXiv:0908.3493] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  64. T. Faulkner and H. Liu, Condensed matter physics of a strongly coupled gauge theory with quarks: Some novel features of the phase diagram, arXiv:0812.4278 [INSPIRE].

  65. I. Amado, M. Kaminski and K. Landsteiner, Hydrodynamics of Holographic Superconductors, JHEP 05 (2009) 021 [arXiv:0903.2209] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  66. L.-Y. Hung and A. Sinha, Holographic quantum liquids in 1 + 1 dimensions, JHEP 01 (2010) 114 [arXiv:0909.3526] [INSPIRE].

    Article  ADS  Google Scholar 

  67. G. Gruner, The dynamics of spin-density waves, Rev. Mod. Phys. 66 (1994) 1 [INSPIRE].

    Article  ADS  Google Scholar 

  68. G. Gruner, The dynamics of charge-density waves, Rev. Mod. Phys. 60 (1988) 1129 [INSPIRE].

    Article  ADS  Google Scholar 

  69. N. Jokela, G. Lifschytz and M. Lippert, Magneto-roton excitation in a holographic quantum Hall fluid, JHEP 02 (2011) 104 [arXiv:1012.1230] [INSPIRE].

    Article  ADS  Google Scholar 

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

    ADS  Google Scholar 

  71. S.A. Hartnoll and A. Tavanfar, Electron stars for holographic metallic criticality, Phys. Rev. D 83 (2011) 046003 [arXiv:1008.2828] [INSPIRE].

    ADS  Google Scholar 

  72. V.G.M. Puletti, S. Nowling, L. Thorlacius and T. Zingg, Holographic metals at finite temperature, JHEP 01 (2011) 117 [arXiv:1011.6261] [INSPIRE].

    Article  ADS  Google Scholar 

  73. J.L. Davis, H. Omid and G.W. Semenoff, Holographic Fermionic Fixed Points in D = 3, JHEP 09 (2011) 124 [arXiv:1107.4397] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  74. G. Grignani, N. Kim and G.W. Semenoff, D7-anti-D7 bilayer: holographic dynamical symmetry breaking, arXiv:1208.0867 [INSPIRE].

  75. H. Omid and G.W. Semenoff, D3-D7 Holographic dual of a perturbed 3D CFT, arXiv:1208.5176 [INSPIRE].

  76. C. Kristjansen, G.W. Semenoff and D. Young, Chiral primary one-point functions in the D3-D7 defect conformal field theory, JHEP 01 (2013) 117 [arXiv:1210.7015] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Departamento de Física de Partículas, Universidade de Santiago de Compostela, and Instituto Galego de Física de Altas Enerxías (IGFAE), E-15782, Santiago de Compostela, Spain

    Niko Jokela

  2. Crete Center for Theoretical Physics, Department of Physics, University of Crete, 71003, Heraklion, Greece

    Matti Järvinen & Matthew Lippert

  3. Institute for Theoretical Physics, University of Amsterdam, 1090GL, Amsterdam, Netherlands

    Matthew Lippert

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  1. Niko Jokela
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  2. Matti Järvinen
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Correspondence to Matthew Lippert.

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ArXiv ePrint: 1211.1381

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Jokela, N., Järvinen, M. & Lippert, M. Fluctuations and instabilities of a holographic metal. J. High Energ. Phys. 2013, 7 (2013). https://doi.org/10.1007/JHEP02(2013)007

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