Towards a field-theory interpretation of bottom-up holography

  • V. P. J. Jacobs
  • S. Grubinskas
  • H. T. C. Stoof
Open Access
Regular Article - Theoretical Physics

Abstract

We investigate recent results for the electrical conductivity and the fermionic self-energy, obtained in a holographic bottom-up model for a relativistic charge-neutral conformal field theory. We present two possible field-theoretic derivations of these results, using either a semiholographic or a holographic point of view. In the semiholographic interpretation, we also show how, in general, the conductivity should be calculated in agreement with Ward identities. The resulting field-theory interpretation may lead to a better understanding of the holographic dictionary in applied AdS/CMT.

Keywords

Effective field theories Holography and condensed matter physics (AdS/CMT) 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    H.v. Lohneysen, A. Rosch, M. Vojta and P. Wölfle, Fermi-liquid instabilities at magnetic quantum phase transitions, Rev. Mod. Phys. 79 (2007) 1015 [INSPIRE].
  2. [2]
    S.L. Sondhi, S.M. Girvin, J.P. Carini and D. Shahar, Continuous quantum phase transitions, Rev. Mod. Phys. 69 (1997) 315 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    S. Sachdev, Quantum Phase Transitions, Cambridge University Press, Cambridge U.K. (1999).MATHGoogle Scholar
  4. [4]
    M. Vojta, Quantum phase transitions, Rep. Prog. Phys. 66 (2003) 2069.ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    W. Zwerger, The BCS-BEC Crossover and the Unitary Fermi Gas, Springer-Verlag Berlin Heidelberg, Germany (2012).CrossRefGoogle Scholar
  6. [6]
    K.B. Gubbels and H.T.C. Stoof, Imbalanced Fermi gases at unitarity, Phys. Rept. 525 (2013) 255 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    K.B. Gubbels and H.T.C. Stoof, Renormalization Group Theory for the Imbalanced Fermi Gas, Phys. Rev. Lett. 100 (2008) 140407 [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    K. Damle and S. Sachdev, Nonzero-temperature transport near quantum critical points, Phys. Rev. B 56 (1997) 8714.ADSCrossRefGoogle Scholar
  9. [9]
    C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].MathSciNetMATHGoogle Scholar
  10. [10]
    S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    J. McGreevy, Holographic duality with a view toward many-body physics, Adv. High Energy Phys. 2010 (2010) 723105.CrossRefMATHGoogle Scholar
  12. [12]
    U. Gürsoy, E. Plauschinn, H. Stoof and S. Vandoren, Holography and ARPES Sum-Rules, JHEP 05 (2012) 018 [arXiv:1112.5074] [INSPIRE].CrossRefGoogle Scholar
  13. [13]
    U. Gürsoy, V. Jacobs, E. Plauschinn, H. Stoof and S. Vandoren, Holographic models for undoped Weyl semimetals, JHEP 04 (2013) 127 [arXiv:1209.2593] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    T. Faulkner and J. Polchinski, Semi-Holographic Fermi Liquids, JHEP 06 (2011) 012 [arXiv:1001.5049] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  15. [15]
    J. Erdmenger, C. Hoyos, A. O’Bannon and J. Wu, A Holographic Model of the Kondo Effect, JHEP 12 (2013) 086 [arXiv:1310.3271] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    C. Charmousis, B. Gouteraux, B.S. Kim, E. Kiritsis and R. Meyer, Effective Holographic Theories for low-temperature condensed matter systems, JHEP 11 (2010) 151 [arXiv:1005.4690] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  17. [17]
    H. Liu, Scattering in anti-de Sitter space and operator product expansion, Phys. Rev. D 60 (1999) 106005 [hep-th/9811152] [INSPIRE].ADSGoogle Scholar
  18. [18]
    V. Balasubramanian, S.B. Giddings and A.E. Lawrence, What do CFTs tell us about Anti-de Sitter space-times?, JHEP 03 (1999) 001 [hep-th/9902052] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  19. [19]
    E. D’Hoker, S.D. Mathur, A. Matusis and L. Rastelli, The Operator product expansion of N = 4 SYM and the 4 point functions of supergravity, Nucl. Phys. B 589 (2000) 38 [hep-th/9911222] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  20. [20]
    I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, Holography from Conformal Field Theory, JHEP 10 (2009) 079 [arXiv:0907.0151] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  21. [21]
    A.L. Fitzpatrick, E. Katz, D. Poland and D. Simmons-Duffin, Effective Conformal Theory and the Flat-Space Limit of AdS, JHEP 07 (2011) 023 [arXiv:1007.2412] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  22. [22]
    S. El-Showk and K. Papadodimas, Emergent Spacetime and Holographic CFTs, JHEP 10 (2012) 106 [arXiv:1101.4163] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    P. Kovtun and A. Ritz, Universal conductivity and central charges, Phys. Rev. D 78 (2008) 066009 [arXiv:0806.0110] [INSPIRE].ADSGoogle Scholar
  24. [24]
    V.P.J. Jacobs, S.J.G. Vandoren and H.T.C. Stoof, Holographic interaction effects on transport in Dirac semimetals, Phys. Rev. B 90 (2014) 045108 [arXiv:1403.3608] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    Y. Huh, P. Strack and S. Sachdev, Conserved current correlators of conformal field theories in 2+1 dimensions, Phys. Rev. B 88 (2013) 155109 [arXiv:1307.6863] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    U. Gürsoy and P. Betzios, Fermionic Greens functions in an electromagnetic background, work in progress.Google Scholar
  27. [27]
    S.-S. Lee, A Non-Fermi Liquid from a Charged Black Hole: A Critical Fermi Ball, Phys. Rev. D 79 (2009) 086006 [arXiv:0809.3402] [INSPIRE].ADSGoogle Scholar
  28. [28]
    M. Cubrovic, J. Zaanen and K. Schalm, String Theory, Quantum Phase Transitions and the Emergent Fermi-Liquid, Science 325 (2009) 439 [arXiv:0904.1993] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  29. [29]
    S.A. Hartnoll and A. Tavanfar, Electron stars for holographic metallic criticality, Phys. Rev. D 83 (2011) 046003 [arXiv:1008.2828] [INSPIRE].ADSGoogle Scholar
  30. [30]
    V.G.M. Puletti, S. Nowling, L. Thorlacius and T. Zingg, Holographic metals at finite temperature, JHEP 01 (2011) 117 [arXiv:1011.6261] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  31. [31]
    T. Faulkner, N. Iqbal, H. Liu, J. McGreevy and D. Vegh, Charge transport by holographic Fermi surfaces, Phys. Rev. D 88 (2013) 045016 [arXiv:1306.6396] [INSPIRE].ADSGoogle Scholar
  32. [32]
    U.H. Danielsson and L. Thorlacius, Black holes in asymptotically Lifshitz spacetime, JHEP 03 (2009) 070 [arXiv:0812.5088] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  33. [33]
    J. Tarrio and S. Vandoren, Black holes and black branes in Lifshitz spacetimes, JHEP 09 (2011) 017 [arXiv:1105.6335] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  34. [34]
    D.Z. Freedman and A. van Proeyen, Supergravity, Cambridge University Press, Cambridge U.K. (2012).CrossRefMATHGoogle Scholar
  35. [35]
    C.G. Bollini, J.J. Giambiagi and A.G. Domínguez, Analytic regularization and the divergences of quantum field theories, Il Nuovo Cimento Series 10 31 (1964) 550.Google Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  • V. P. J. Jacobs
    • 1
  • S. Grubinskas
    • 1
  • H. T. C. Stoof
    • 1
  1. 1.Institute for Theoretical Physics and Center for Extreme Matter and Emergent PhenomenaUtrecht UniversityUtrechtThe Netherlands

Personalised recommendations