Skip to main content
SpringerLink
Log in

Monopoles and holography

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We present a holographic theory in AdS 4 whose zero temperature ground state develops a crystal structure, spontaneously breaking translational symmetry. The crystal is induced by a background magnetic field, but requires no chemical potential. This lattice arises from the existence of ’t Hooft-Polyakov monopole solitons in the bulk which condense to form a classical object known as a monopole wall. In the infra-red, the magnetic field is screened and there is an emergent SU(2) global symmetry.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. Iqbal, H. Liu, M. Mezei and Q. Si, Quantum phase transitions in holographic models of magnetism and superconductors, Phys. Rev. D 82 (2010) 045002 [arXiv:1003.0010] [SPIRES].

    ADS  Google Scholar 

  2. S. Bolognesi, Multimonopoles, magnetic bags, Nucl. Phys. B 752 (2006) 93 [hep-th/0512133] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  3. R.S. Ward, A monopole wall, Phys. Rev. D 75 (2007) 021701 [hep-th/0612047] [SPIRES].

    ADS  Google Scholar 

  4. S.S. Gubser, Breaking an abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [SPIRES].

    ADS  Google Scholar 

  5. S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a holographic superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [SPIRES].

    Article  ADS  Google Scholar 

  6. S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  7. S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  8. G.T. Horowitz, Introduction to holographic superconductors, arXiv:1002.1722 [SPIRES].

  9. S.A. Hartnoll and P. Kovtun, Hall conductivity from dyonic black holes, Phys. Rev. D 76 (2007) 066001 [arXiv:0704.1160] [SPIRES].

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  11. S.S. Gubser, Colorful horizons with charge in Anti-de Sitter space, Phys. Rev. Lett. 101 (2008) 191601 [arXiv:0803.3483] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  12. S.S. Gubser and S.S. Pufu, The gravity dual of a p-wave superconductor, JHEP 11 (2008) 033 [arXiv:0805.2960] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  13. J.A. Harvey, Magnetic monopoles, duality and supersymmetry, hep-th/9603086 [SPIRES].

  14. A.R. Lugo and F.A. Schaposnik, Monopole and dyon solutions in AdS space, Phys. Lett. B 467 (1999) 43 [hep-th/9909226] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  15. A.R. Lugo, E.F. Moreno and F.A. Schaposnik, Monopole solutions in AdS space, Phys. Lett. B 473 (2000) 35 [hep-th/9911209] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  16. D. Allahbakhshi and F. Ardalan, Holographic phase transition to topological dyons, JHEP 10 (2010) 114 [arXiv:1007.4451] [SPIRES].

    Article  ADS  Google Scholar 

  17. E. Radu and D.H. Tchrakian, New axially symmetric Yang-Mills-Higgs solutions with negative cosmological constant, Phys. Rev. D 71 (2005) 064002 [hep-th/0411084] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  18. V. Borokhov, A. Kapustin and X.-k. Wu, Topological disorder operators in three-dimensional conformal field theory, JHEP 11 (2002) 049 [hep-th/0206054] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  19. E. Witten, SL(2,Z ) action on three-dimensional conformal field theories with abelian symmetry, hep-th/0307041 [SPIRES].

  20. D. Marolf and S.F. Ross, Boundary conditions and new dualities: vector fields in AdS/CFT, JHEP 11 (2006) 085 [hep-th/0606113] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  21. E.J. Weinberg and A.H. Guth, Nonexistence of spherically symmetric monopoles with multiple magnetic charge, Phys. Rev. D 14 (1976) 1660 [SPIRES].

    ADS  Google Scholar 

  22. N.J. Hitchin, N.S. Manton and M.K. Murray, Symmetric monopoles, Nonlinearity 8 (1995) 661 [dg-ga/9503016] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  23. C.J. Houghton and P.M. Sutcliffe, Octahedral and dodecahedral monopoles, hep-th/9601147 [SPIRES].

  24. C.J. Houghton, N.S. Manton and P.M. Sutcliffe, Rational maps, monopoles and skyrmions, Nucl. Phys. B 510 (1998) 507 [hep-th/9705151] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  25. R.A. Battye, C.J. Houghton and P.M. Sutcliffe, Icosahedral skyrmions, J. Math. Phys. 44 (2003) 3543 [hep-th/0210147] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  26. J. Silva Lobo and R.S. Ward, Skyrmion multi-walls, J. Phys. A 42 (2009) 482001 [arXiv:0910.5457] [SPIRES].

    MathSciNet  Google Scholar 

  27. R.S. Ward, private communication.

  28. S. Cherkis and R.S. Ward, to appear.

  29. S. Kachru, A. Karch and S. Yaida, Holographic lattices, dimers and glasses, Phys. Rev. D 81 (2010) 026007 [arXiv:0909.2639] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  30. A. Aperis et al., Holographic charge density waves, arXiv:1009.6179 [SPIRES].

  31. R. Flauger, E. Pajer and S. Papanikolaou, A striped holographic superconductor, arXiv:1010.1775 [SPIRES].

  32. S.L. Sondhi, A. Karlhede, S.A. Kivelson and E.H. Rezayi, Skyrmions and the crossover from the integer to fractional quantum Hall effect at small Zeeman energies, Phys. Rev. B 47 (1993) 16419 [SPIRES].

    ADS  Google Scholar 

  33. K. Yang, S. Das Sarma and A.H. MacDonald, Collective modes and skyrmion excitations in graphene SU(4) quantum Hall ferromagnets, Phys. Rev. B 74 (2006) 075423 [cond-mat/0605666].

    ADS  Google Scholar 

  34. K. Maeda, M. Natsuume and T. Okamura, Vortex lattice for a holographic superconductor, Phys. Rev. D 81 (2010) 026002 [arXiv:0910.4475] [SPIRES].

    ADS  Google Scholar 

  35. S. Nakamura, H. Ooguri and C.-S. Park, Gravity dual of spatially modulated phase, Phys. Rev. D 81 (2010) 044018 [arXiv:0911.0679] [SPIRES].

    ADS  Google Scholar 

  36. H. Ooguri and C.-S. Park, Holographic end-point of spatially modulated phase transition, Phys. Rev. D 82 (2010) 126001 [arXiv:1007.3737] [SPIRES].

    ADS  Google Scholar 

  37. K.-M. Lee and E.J. Weinberg, BPS magnetic monopole bags, Phys. Rev. D 79 (2009) 025013 [arXiv:0810.4962] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  38. F. Denef and S.A. Hartnoll, Landscape of superconducting membranes, Phys. Rev. D 79 (2009) 126008 [arXiv:0901.1160] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  39. S. Bolognesi, Magnetic bags and black holes, Nucl. Phys. B 845 (2011) 324 [arXiv:1005.4642] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  40. S.S. Gubser and F.D. Rocha, The gravity dual to a quantum critical point with spontaneous symmetry breaking, Phys. Rev. Lett. 102 (2009) 061601 [arXiv:0807.1737] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  41. N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa, The string landscape, black holes and gravity as the weakest force, JHEP 06 (2007) 060 [hep-th/0601001] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, U.K.

    Stefano Bolognesi & David Tong

Authors
  1. Stefano Bolognesi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David Tong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to David Tong.

Additional information

ArXiv ePrint: 1010.4178

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bolognesi, S., Tong, D. Monopoles and holography. J. High Energ. Phys. 2011, 153 (2011). https://doi.org/10.1007/JHEP01(2011)153

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP01(2011)153

Keywords

Search

Navigation