Journal of High Energy Physics

, 2013:116 | Cite as

Vacuum instability in electric fields via AdS/CFT: Euler-Heisenberg Lagrangian and Planckian thermalization

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Abstract

We analyze vacuum instability of strongly coupled gauge theories in a constant electric field using AdS/CFT correspondence. The model is the \( \mathcal{N}=2 \) 1-flavor supersymmetric large N c QCD in the strong ’t Hooft coupling limit. We calculate the Euler-Heisenberg effective Lagrangian \( \mathcal{L} \)(E), which encodes the nonlinear response and the quantum decay rate of the vacuum in a background electric field E, from the complex D-brane action in AdS/CFT. We find that the decay rate given by Im \( \mathcal{L} \)(E) becomes nonzero above a critical electric field set by the confining force between quarks. A large E expansion of Im \( \mathcal{L} \)(E) is found to coincide with that of the Schwinger effects in QED, replacing its electron mass by the confining force. Then, the time-dependent response of the system in a strong electric field is solved non-perturbatively, and we observe a universal thermalization at a shortest timescale “Planckian thermalization time” \( {\tau_{\mathrm{th}}}\sim \frac{\hbar }{{{k_B}T_{\mathrm{eff}}^{\infty }}}\sim \frac{\hbar }{{{k_B}}}{E^{{-{1 \left/ {2} \right.}}}} \). Here, \( T_{\mathrm{eff}}^{\infty } \) is an effective temperature which quarks feel in the nonequilibrium state with nonzero electric current, calculated in AdS/CFT as a Hawking temperature. Stronger electric fields accelerate the thermalization, and for a realistic value of the electric field in RHIC experiment, we obtain τ th ~ 1 [fm/c], which is consistent with the believed value.

Keywords

AdS-CFT Correspondence Holography and quark-gluon plasmas Holography and condensed matter physics (AdS/CMT) 
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References

  1. [1]
    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] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    K. Yagi, T. Hatsuda and Y. Miake, Quark-Gluon Plasma, Cambridge University Press, Cambridge U.K. (2005).Google Scholar
  3. [3]
    F. Gelis, E. Iancu, J. Jalilian-Marian and R. Venugopalan, The Color Glass Condensate, Ann. Rev. Nucl. Part. Sci. 60 (2010) 463 [arXiv:1002.0333] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    T. Lappi and L. McLerran, Some features of the glasma, Nucl. Phys. A 772 (2006) 200 [hep-ph/0602189] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    T. Oka and H. Aoki, Ground-State Decay Rate for the Zener Breakdown in Band and Mott Insulators, Phys. Rev. Lett. 95 (2005) 137601.ADSCrossRefGoogle Scholar
  6. [6]
    T. Oka and H. Aoki, Nonequilibrium Quantum Breakdown in a Strongly Correlated Electron System, in Lecture Notes in Physics. Vol. Quantum and Semi-classical Percolation and Breakdown in Disordered Solids, Springer, Berlin Germany (2009), pg. 1.Google Scholar
  7. [7]
    T. Oka, R. Arita and H. Aoki, Breakdown of a Mott insulator — non-adiabatic tunneling mechanism, Phys. Rev. Lett. 91 (2003) 066406.ADSCrossRefGoogle Scholar
  8. [8]
    M. Eckstein, T. Oka and P. Werner, Dielectric Breakdown of Mott Insulators in Dynamical Mean-Field Theory, Phys. Rev. Lett. 105 (2010) 146404.ADSCrossRefGoogle Scholar
  9. [9]
    A. Mitra, S. Takei, Y.B. Kim and A.J. Millis, Nonequilibrium Quantum Criticality in Open Electronic Systems, Phys. Rev. Lett. 97 (2006) 236808.ADSCrossRefGoogle Scholar
  10. [10]
    A. Mitra and A. Millis, Current-driven quantum criticality in itinerant electron ferromagnets, Phys. Rev. B 77 (2008) 220404.ADSCrossRefGoogle Scholar
  11. [11]
    D. Dalidovich and P. Phillips, Nonlinear transport near a quantum phase transition in two dimensions, Phys. Rev. Lett. 93 (2004) 027004.ADSCrossRefGoogle Scholar
  12. [12]
    A. Karch and S. Sondhi, Non-linear, finite frequency quantum critical transport from AdS/CFT, JHEP 01 (2011) 149 [arXiv:1008.4134] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    A.G. Green and S.L. Sondhi, Nonlinear Quantum Critical Transport and the Schwinger Mechanism for a Superfluid-Mott-Insulator Transition of Bosons, Phys. Rev. Lett. 95 (2005) 267001.ADSCrossRefGoogle Scholar
  14. [14]
    J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].
  15. [15]
    S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].MathSciNetADSMATHGoogle Scholar
  17. [17]
    W. Heisenberg and H. Euler, Folgerungen aus der Diracschen Theorie des Positrons, Z. Physik 98 (1936) 714.ADSCrossRefGoogle Scholar
  18. [18]
    V. Weisskipf, in The electrodynamics of the vacuum based on the quantum theory of the electron, Kong. Dans. Vid. Selsk. Math-fys. Medd. XIV No. 6 (1936), English translation in: Early Quantum Electrodynamics: A Source Book, A.I. Miller eds., Cambridge University Press, Cambridge U.K. (1994).Google Scholar
  19. [19]
    J.S. Schwinger, On gauge invariance and vacuum polarization, Phys. Rev. 82 (1951) 664 [INSPIRE].MathSciNetADSCrossRefMATHGoogle Scholar
  20. [20]
    G.V. Dunne, Heisenberg-Euler Effective Lagrangians: Basics and Extensions, hep-th/0406216.
  21. [21]
    W. Dittrich and H. Gies, Probing the Quantum Vacuum, Springer-Verlag, Berlin Germany (2000).Google Scholar
  22. [22]
    S.R. Coleman, More about the massive Schwinger model, Annals Phys. 101 (1976) 239 [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  24. [24]
    C. Bachas and M. Porrati, Pair creation of open strings in an electric field, Phys. Lett. B 296 (1992) 77 [hep-th/9209032] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  25. [25]
    C. Bachas, D-brane dynamics, Phys. Lett. B 374 (1996) 37 [hep-th/9511043] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  26. [26]
    G.W. Semenoff and K. Zarembo, Holographic Schwinger effect, Phys. Rev. Lett. 107 (2011) 171601 [arXiv:1109.2920] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    E. Fradkin and A.A. Tseytlin, Nonlinear electrodynamics from quantized strings, Phys. Lett. B 163 (1985) 123 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  28. [28]
    K.-Y. Kim, S.-J. Sin and I. Zahed, Dense and hot holographic QCD: finite baryonic E field, JHEP 07 (2008) 096 [arXiv:0803.0318] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    S.R. Das, T. Nishioka and T. Takayanagi, Probe branes, time-dependent couplings and thermalization in AdS/CFT, JHEP 07 (2010) 071 [arXiv:1005.3348] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  30. [30]
    K. Hashimoto, N. Iizuka and T. Oka, Rapid Thermalization by Baryon Injection in Gauge/Gravity Duality, Phys. Rev. D 84 (2011) 066005 [arXiv:1012.4463] [INSPIRE].ADSGoogle Scholar
  31. [31]
    U.H. Danielsson, E. Keski-Vakkuri and M. Kruczenski, Black hole formation in AdS and thermalization on the boundary, JHEP 02 (2000) 039 [hep-th/9912209] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  32. [32]
    S. Bhattacharyya and S. Minwalla, Weak field black hole formation in asymptotically AdS spacetimes, JHEP 09 (2009) 034 [arXiv:0904.0464] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  33. [33]
    R.A. Janik and R.B. Peschanski, Gauge/gravity duality and thermalization of a boost-invariant perfect fluid, Phys. Rev. D 74 (2006) 046007 [hep-th/0606149] [INSPIRE].MathSciNetADSGoogle Scholar
  34. [34]
    H. Ebrahim and M. Headrick, Instantaneous Thermalization in Holographic Plasmas, arXiv:1010.5443 [INSPIRE].
  35. [35]
    J. Abajo-Arrastia, J. Aparicio and E. Lopez, Holographic evolution of entanglement entropy, JHEP 11 (2010) 149 [arXiv:1006.4090] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    V. Balasubramanian et al., Thermalization of Strongly Coupled Field Theories, Phys. Rev. Lett. 106 (2011) 191601 [arXiv:1012.4753] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    A. Buchel, L. Lehner and R.C. Myers, Thermal quenches in N = 2∗ plasmas, JHEP 08 (2012) 049 [arXiv:1206.6785] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    M.P. Heller, D. Mateos, W. van der Schee and D. Trancanelli, Strong Coupling Isotropization of Non-Abelian Plasmas Simplified, Phys. Rev. Lett. 108 (2012) 191601 [arXiv:1202.0981] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    V. Balasubramanian et al., Inhomogeneous Thermalization in Strongly Coupled Field Theories, arXiv:1307.1487 [INSPIRE].
  40. [40]
    A. Buchel, L. Lehner, R.C. Myers and A. van Niekerk, Quantum quenches of holographic plasmas, JHEP 05 (2013) 067 [arXiv:1302.2924] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    A. Buchel, R.C. Myers and A. van Niekerk, Universality of Abrupt Holographic Quenches, arXiv:1307.4740 [INSPIRE].
  42. [42]
    J. Ambjørn and Y. Makeenko, Remarks on Holographic Wilson Loops and the Schwinger Effect, Phys. Rev. D 85 (2012) 061901 [arXiv:1112.5606] [INSPIRE].ADSGoogle Scholar
  43. [43]
    S. Bolognesi, F. Kiefer and E. Rabinovici, Comments on Critical Electric and Magnetic Fields from Holography, JHEP 01 (2013) 174 [arXiv:1210.4170] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    Y. Sato and K. Yoshida, Holographic description of the Schwinger effect in electric and magnetic fields, JHEP 04 (2013) 111 [arXiv:1303.0112] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  45. [45]
    Y. Sato and K. Yoshida, Potential Analysis in Holographic Schwinger Effect, arXiv:1304.7917 [INSPIRE].
  46. [46]
    Y. Sato and K. Yoshida, Holographic Schwinger effect in confining phase, JHEP 09 (2013) 134 [arXiv:1306.5512] [INSPIRE].CrossRefADSGoogle Scholar
  47. [47]
    A. Karch and A. O’Bannon, Metallic AdS/CFT, JHEP 09 (2007) 024 [arXiv:0705.3870] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  48. [48]
    T. Albash, V.G. Filev, C.V. Johnson and A. Kundu, Quarks in an external electric field in finite temperature large-N gauge theory, JHEP 08 (2008) 092 [arXiv:0709.1554] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  49. [49]
    J. Erdmenger, N. Evans, I. Kirsch and E. Threlfall, Mesons in gauge/gravity duals — a review, Eur. Phys. J. A 35 (2008) 81 [arXiv:0711.4467] [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    O. Bergman, G. Lifschytz and M. Lippert, Response of holographic QCD to electric and magnetic fields, JHEP 05 (2008) 007 [arXiv:0802.3720] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    C.V. Johnson and A. Kundu, External fields and chiral symmetry breaking in the Sakai-Sugimoto model, JHEP 12 (2008) 053 [arXiv:0803.0038] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  52. [52]
    A. Karch and A. O’Bannon, Holographic thermodynamics at finite baryon density: some exact results, JHEP 11 (2007) 074 [arXiv:0709.0570] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  53. [53]
    J. Erdmenger, R. Meyer and J.P. Shock, AdS/CFT with flavour in electric and magnetic Kalb-Ramond fields, JHEP 12 (2007) 091 [arXiv:0709.1551] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  54. [54]
    C. Herzog, A. Karch, P. Kovtun, C. Kozcaz and L. Yaffe, Energy loss of a heavy quark moving through N = 4 supersymmetric Yang-Mills plasma, JHEP 07 (2006) 013 [hep-th/0605158] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  55. [55]
    S.S. Guser, Drag force in AdS/CFT, Phys. Rev. D 74 (2006) 126005 [hep-th/0605182] [INSPIRE].ADSGoogle Scholar
  56. [56]
    C. Burgess, Open String Instability in Background Electric Fields, Nucl. Phys. B 294 (1987) 427 [INSPIRE].ADSCrossRefGoogle Scholar
  57. [57]
    V. Nesterenko, The Dynamics of Open Strings in a Background Electromagnetic Field, Int. J. Mod. Phys. A 4 (1989) 2627 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  58. [58]
    M. Bianchi, D.Z. Freedman and K. Skenderis, Holographic renormalization, Nucl. Phys. B 631 (2002) 159 [hep-th/0112119] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  59. [59]
    A. Karch, A. O’Bannon and K. Skenderis, Holographic renormalization of probe D-branes in AdS/CFT, JHEP 04 (2006) 015 [hep-th/0512125] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  60. [60]
    M. Kruczenski, D. Mateos, R.C. Myers and D.J. Winters, Meson spectroscopy in AdS/CFT with flavor, JHEP 07 (2003) 049 [hep-th/0304032] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  61. [61]
    K.-Y. Kim, J.P. Shock and J. Tarrio, The open string membrane paradigm with external electromagnetic fields, JHEP 06 (2011) 017 [arXiv:1103.4581] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  62. [62]
    W. Unruh, Notes on black hole evaporation, Phys. Rev. D 14 (1976) 870 [INSPIRE].ADSGoogle Scholar
  63. [63]
    J. Sonner and A.G. Green, Hawking Radiation and Non-equilibrium Quantum Critical Current Noise, Phys. Rev. Lett. 109 (2012) 091601 [arXiv:1203.4908] [INSPIRE].ADSCrossRefGoogle Scholar
  64. [64]
    J. Zaanen, Superconductivity: why the temperature is high, Nature 430 (2004) 512.ADSCrossRefGoogle Scholar
  65. [65]
    V. Skokov, A.Y. Illarionov and V. Toneev, Estimate of the magnetic field strength in heavy-ion collisions, Int. J. Mod. Phys. A 24 (2009) 5925 [arXiv:0907.1396] [INSPIRE].ADSCrossRefGoogle Scholar
  66. [66]
    V. Voronyuk et al., (Electro-)magnetic field evolution in relativistic heavy-ion collisions, Phys. Rev. C 83 (2011) 054911 [arXiv:1103.4239] [INSPIRE].ADSGoogle Scholar
  67. [67]
    A. Bzdak and V. Skokov, Event-by-event fluctuations of magnetic and electric fields in heavy ion collisions, Phys. Lett. B 710 (2012) 171 [arXiv:1111.1949] [INSPIRE].ADSCrossRefGoogle Scholar
  68. [68]
    W.-T. Deng and X.-G. Huang, Event-by-event generation of electromagnetic fields in heavy-ion collisions, Phys. Rev. C 85 (2012) 044907 [arXiv:1201.5108] [INSPIRE].ADSGoogle Scholar
  69. [69]
    P. Kovtun, D. Son and A. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev. Lett. 94 (2005) 111601 [hep-th/0405231] [INSPIRE].ADSCrossRefGoogle Scholar
  70. [70]
    U.W. Heinz, Thermalization at RHIC, AIP Conf. Proc. 739 (2005) 163 [nucl-th/0407067] [INSPIRE].ADSCrossRefGoogle Scholar
  71. [71]
    P.M. Chesler and L.G. Yaffe, Horizon formation and far-from-equilibrium isotropization in supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 102 (2009) 211601 [arXiv:0812.2053] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  72. [72]
    V. Ritus, Method of eigenfunctions and mass operator in quantum electrodynamics of a constant field, Sov. Phys. JETP 48 (1978) 788 [INSPIRE].ADSGoogle Scholar
  73. [73]
    S. Lebedev and V. Ritus, Virial representation of the imaginary part of the lagrange function of the electromagnetic field, Sov. Phys. JETP 59 (1984) 237 [INSPIRE].Google Scholar
  74. [74]
    I.K. Affleck, O. Alvarez and N.S. Manton, Pair Production at Strong Coupling in Weak External Fields, Nucl. Phys. B 197 (1982) 509 [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.Department of PhysicsOsaka UniversityToyonakaJapan
  2. 2.Department of Applied PhysicsUniversity of TokyoTokyoJapan
  3. 3.Mathematical Physics Lab., RIKEN Nishina CenterSaitamaJapan

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