Particle-vortex duality and theta terms in AdS/CMT applications

  • Luis Alejo
  • Horatiu NastaseEmail author
Open Access
Regular Article - Theoretical Physics


In this paper we study particle-vortex duality and the effect of theta terms from the point of view of AdS/CMT constructions. We can construct the duality in 2+1 dimensional field theories with or without a Chern-Simons term, and derive an effect on conductivities, when the action is viewed as a response action. We can find its effect on 3+1 dimensional theories, with or without a theta term, coupled to gravity in asymptotically AdS space, and derive the resulting effect on conductivities defined in the spirit of AdS/CFT. AdS/CFT then relates the 2+1 dimensional and the 3+1 dimensional cases naturally. Quantum gravity corrections, as well as more general effective actions for the abelian vector, can be treated similarly. We can use the fluid/gravity correspondence, and the membrane paradigm, to define shear and bulk viscosities η and ζ for a gravity plus abelian vector plus scalar system near a black hole, and define the effect of the S-duality on it.


AdS-CFT Correspondence Holography and condensed matter physics (AdS/CMT) 


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


  1. [1]
    A. Zee, Quantum field theory in a nutshell, Princeton University Press, Princeton U.S.A. (2010).zbMATHGoogle Scholar
  2. [2]
    J. Murugan and H. Nastase, Particle-vortex duality in topological insulators and superconductors, JHEP05 (2017) 159 [arXiv:1606.01912] [INSPIRE].
  3. [3]
    A. Karch and D. Tong, Particle-Vortex Duality from 3d Bosonization, Phys. Rev.X 6 (2016) 031043 [arXiv:1606.01893] [INSPIRE].
  4. [4]
    N. Seiberg, T. Senthil, C. Wang and E. Witten, A Duality Web in 2 + 1 Dimensions and Condensed Matter Physics, Annals Phys.374 (2016) 395 [arXiv:1606.01989] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    C. Dasgupta and B.I. Halperin, Phase Transition in a Lattice Model of Superconductivity, Phys. Rev. Lett.47 (1981) 1556 [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    M.E. Peskin, Mandelstamt Hooft Duality in Abelian Lattice Models, Annals Phys.113 (1978) 122 [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    D.H. Lee and M.P.A. Fisher, Anyon superconductivity and the fractional quantum Hall effect, Phys. Rev. Lett.63 (1989) 903 [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    E.C. Marino, Quantum Theory of Nonlocal Vortex Fields, Phys. Rev.D 38 (1988) 3194 [INSPIRE].ADSMathSciNetGoogle Scholar
  9. [9]
    E.C. Marino, Duality, quantum vortices and anyons in Maxwell-Chern-Simons-Higgs theories, Annals Phys.224 (1993) 225 [hep-th/9208062] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    C.P. Burgess and B.P. Dolan, Particle vortex duality and the modular group: Applications to the quantum Hall effect and other 2 − D systems, Phys. Rev.B 63 (2001) 155309 [hep-th/0010246] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    J. Murugan, H. Nastase, N. Rughoonauth and J.P. Shock, Particle-vortex and Maxwell duality in the AdS 4 × ℂℙ3/ABJM correspondence, JHEP10 (2014) 51 [arXiv:1404.5926] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    R.O. Ramos, J.F. Medeiros Neto, D.G. Barci and C.A. Linhares, Abelian Higgs model effective potential in the presence of vortices, Phys. Rev. D72 (2005) 103524 [hep-th/0506052] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    R.O. Ramos and J.F. Medeiros Neto, Transition Point for Vortex Condensation in the Chern-Simons Higgs Model, Phys. Lett. B666 (2008) 496 [arXiv:0711.0798] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys.38 (1999) 1113 [hep-th/9711200] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  15. [15]
    H. Nastase, Introduction to the ADS/CFT Correspondence, Cambridge University Press, Cambridge U.K. (2015).CrossRefGoogle Scholar
  16. [16]
    M. Ammon and J. Erdmenger, Gauge/gravity duality, Cambridge University Press, Cambridge U.K. (2015).Google Scholar
  17. [17]
    H. Nastase, Towards deriving the AdS/CFT correspondence, arXiv:1812.10347 [INSPIRE].
  18. [18]
    E. Witten, SL(2, ℤ) action on three-dimensional conformal field theories with Abelian symmetry, hep-th/0307041 [INSPIRE].
  19. [19]
    C.P. Herzog, P. Kovtun, S. Sachdev and D.T. Son, Quantum critical transport, duality and M-theory, Phys. Rev.D 75 (2007) 085020 [hep-th/0701036] [INSPIRE].ADSMathSciNetGoogle Scholar
  20. [20]
    O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP10 (2008) 091 [arXiv:0806.1218] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  21. [21]
    J.C. Le Guillou, E. Moreno, C. Núñez and F.A. Schaposnik, NonAbelian bosonization in two-dimensions and three-dimensions, Nucl. Phys.B 484 (1997) 682 [hep-th/9609202] [INSPIRE].
  22. [22]
    J.C. Le Guillou, E. Moreno, C. Núñez and F.A. Schaposnik, On three-dimensional bosonization, Phys. Lett.B 409 (1997) 257 [hep-th/9703048] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  23. [23]
    H. Nastase, String Theory Methods for Condensed Matter Physics, Cambridge University Press, Cambridge U.K. (2017).CrossRefGoogle Scholar
  24. [24]
    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].
  25. [25]
    C. Lopez-Arcos, H. Nastase, F. Rojas and J. Murugan, Conductivity in the gravity dual to massive ABJM and the membrane paradigm, JHEP01 (2014) 036 [arXiv:1306.1263] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    P. Kovtun, D.T. Son and A.O. Starinets, Holography and hydrodynamics: Diffusion on stretched horizons, JHEP10 (2003) 064 [hep-th/0309213] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  27. [27]
    M. Brigante, H. Liu, R.C. Myers, S. Shenker and S. Yaida, Viscosity Bound Violation in Higher Derivative Gravity, Phys. Rev. D77 (2008) 126006 [arXiv:0712.0805] [INSPIRE].
  28. [28]
    R.C. Myers, S. Sachdev and A. Singh, Holographic Quantum Critical Transport without Self-Duality, Phys. Rev.D 83 (2011) 066017 [arXiv:1010.0443] [INSPIRE].
  29. [29]
    E. Banks, A. Donos and J.P. Gauntlett, Thermoelectric DC conductivities and Stokes flows on black hole horizons, JHEP10 (2015) 103 [arXiv:1507.00234] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  30. [30]
    A. Donos, J.P. Gauntlett, T. Griffin, N. Lohitsiri and L. Melgar, Holographic DC conductivity and Onsager relations, JHEP07 (2017) 006 [arXiv:1704.05141] [INSPIRE].
  31. [31]
    W. Fischler and S. Kundu, Membrane paradigm, gravitational Θ-term and gauge/gravity duality, JHEP04 (2016) 112 [arXiv:1512.01238] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  32. [32]
    M. Parikh and F. Wilczek, An Action for black hole membranes, Phys. Rev.D 58 (1998) 064011 [gr-qc/9712077] [INSPIRE].
  33. [33]
    S. Deser and R. Jackiw, ’Selfdualityof Topologically Massive Gauge Theories, Phys. Lett. B139 (1984) 371 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  34. [34]
    P.K. Townsend, K. Pilch and P. van Nieuwenhuizen, Selfduality in Odd Dimensions, Phys. Lett.B 136 (1984) 38 [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    X.-L. Qi, T. Hughes and S.-C. Zhang, Topological Field Theory of Time-Reversal Invariant Insulators, Phys. Rev.B 78 (2008) 195424 [arXiv:0802.3537] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    D.T. Son, Is the Composite Fermion a Dirac Particle?, Phys. Rev.X 5 (2015) 031027 [arXiv:1502.03446] [INSPIRE].
  37. [37]
    M. Lippert, R. Meyer and A. Taliotis, A holographic model for the fractional quantum Hall effect, JHEP01 (2015) 023 [arXiv:1409.1369] [INSPIRE].
  38. [38]
    R.H. Price and K.S. Thorne, Membrane Viewpoint on Black Holes: Properties and Evolution of the Stretched Horizon, Phys. Rev.D 33 (1986) 915 [INSPIRE].ADSMathSciNetGoogle Scholar
  39. [39]
    C. Eling and Y. Oz, Relativistic CFT Hydrodynamics from the Membrane Paradigm, JHEP02 (2010) 069 [arXiv:0906.4999] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  40. [40]
    H. Nastase, DBI scalar field theory for QGP hydrodynamics, Phys. Rev.D 94 (2016) 025014 [arXiv:1512.05257] [INSPIRE].
  41. [41]
    S. Endlich, A. Nicolis, R. Rattazzi and J. Wang, The Quantum mechanics of perfect fluids, JHEP04 (2011) 102 [arXiv:1011.6396] [INSPIRE].
  42. [42]
    S. Dubovsky, L. Hui, A. Nicolis and D.T. Son, Effective field theory for hydrodynamics: thermodynamics and the derivative expansion, Phys. Rev. D 85 (2012) 085029 [arXiv:1107.0731] [INSPIRE].
  43. [43]
    L. Berezhiani, J. Khoury and J. Wang, Universe without dark energy: Cosmic acceleration from dark matter-baryon interactions, Phys. Rev.D 95 (2017) 123530 [arXiv:1612.00453] [INSPIRE].
  44. [44]
    S. Mukhi and C. Papageorgakis, M2 to D2, JHEP05 (2008) 085 [arXiv:0803.3218] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Instituto de Física TeóricaUNESP-Universidade Estadual PaulistaSao PauloBrazil

Personalised recommendations