Skip to main content

Chern-Simons vortices and holography

A preprint version of the article is available at arXiv.

Abstract

In this paper, based on the AdS 4 /CFT 3 duality, we have explored the precise connection between the abelian Chern-Simons (CS) Higgs model in (2 + 1) dimensions to that with its dual gravitational counterpart living in one higher dimension. It has been observed that theU(1)current computed at the boundary of the AdS 4 could be expressed as the local function of the vortex solution that has the remarkable structural similarity to that with the Ginzburg-Landau (GL) type local expression for the current associated with the Maxwell-CS type vortices in (2 + 1) dimensions. In order to explore this duality a bit further we have also computed the coherence length as well as the magnetic penetration depth associated with these vortices. Finally using the knowledge of both the coherence length as well as the magnetic penetration depth we have computed the Ginzburg-Landau coefficient for the Maxwell-CS type vortices in (2 + 1) dimensions.

References

  1. S.K. Paul and A. Khare, Charged vortices in abelian Higgs model with Chern-Simons term, Phys. Lett. B 174 (1986) 420 [Erratum ibid. 177B (1986) 453] [INSPIRE].

  2. R. Jackiw and E.J. Weinberg, Selfdual Chern-Simons vortices, Phys. Rev. Lett. 64 (1990) 2234 [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  3. D.P. Jatkar and A. Khare, Peculiar charged vortices in Higgs models with pure Chern-Simons term, Phys. Lett. B 236 (1990) 283 [INSPIRE].

    ADS  Article  Google Scholar 

  4. S.K. Paul and A. Khare, Chern-Simons term by spontaneous symmetry breaking in an abelian Higgs model, Phys. Lett. B 193 (1987) 253 [Erratum ibid. B 196 (1987) 571] [INSPIRE].

  5. R. Banerjee and P. Mukherjee, Spin of Chern-Simons vortices, Nucl. Phys. B 478 (1996) 235 [hep-th/9605226] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  6. J. Hong, Y. Kim and P.Y. Pac, On the multivortex solutions of the abelian Chern-Simons-Higgs theory, Phys. Rev. Lett. 64 (1990) 2230 [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  7. Y. Kim and K.-M. Lee, Vortex dynamics in selfdual Chern-Simons Higgs systems, Phys. Rev. D 49 (1994) 2041 [hep-th/9211035] [INSPIRE].

    ADS  Google Scholar 

  8. L.-B. Fu, Y.-S. Duan and H. Zhang, Evolution of the Chern-Simons vortices, Phys. Rev. D 61 (2000) 045004 [hep-th/0112033] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  9. M. Abou-Zeid and H. Samtleben, Chern-Simons vortices in supergravity, Phys. Rev. D 65 (2002) 085016 [hep-th/0112035] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  10. J.H. Schwarz, Superconformal Chern-Simons theories, JHEP 11 (2004) 078 [hep-th/0411077] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  11. B. Collie and D. Tong, The dynamics of Chern-Simons vortices, Phys. Rev. D 78 (2008) 065013 [arXiv:0805.0602] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  12. F. Navarro-Lerida, E. Radu and D.H. Tchrakian, Non-abelian Chern-Simons-Higgs solutions in (2 + 1) dimensions, Phys. Rev. D 79 (2009) 065036 [arXiv:0811.3524] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  13. D. Bazeia, E. da Hora, C. dos Santos and R. Menezes, Generalized self-dual Chern-Simons vortices, Phys. Rev. D 81 (2010) 125014 [arXiv:1006.3955] [INSPIRE].

    ADS  Google Scholar 

  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].

    MathSciNet  Article  MATH  Google Scholar 

  15. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  MathSciNet  Article  MATH  Google Scholar 

  19. S.S. Gubser, C.P. Herzog, S.S. Pufu and T. Tesileanu, Superconductors from superstrings, Phys. Rev. Lett. 103 (2009) 141601 [arXiv:0907.3510] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  20. J.P. Gauntlett, J. Sonner and T. Wiseman, Quantum criticality and holographic superconductors in M-theory, JHEP 02 (2010) 060 [arXiv:0912.0512] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

  22. J.P. Gauntlett, J. Sonner and T. Wiseman, Holographic superconductivity in M-theory, Phys. Rev. Lett. 103 (2009) 151601 [arXiv:0907.3796] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  23. M. Ammon, J. Erdmenger, M. Kaminski and P. Kerner, Superconductivity from gauge/gravity duality with flavor, Phys. Lett. B 680 (2009) 516 [arXiv:0810.2316] [INSPIRE].

    ADS  Article  Google Scholar 

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

    ADS  Google Scholar 

  25. T. Albash and C.V. Johnson, A holographic superconductor in an external magnetic field, JHEP 09 (2008) 121 [arXiv:0804.3466] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  26. M. Montull, O. Pujolàs, A. Salvio and P.J. Silva, Magnetic response in the holographic insulator/superconductor transition, JHEP 04 (2012) 135 [arXiv:1202.0006] [INSPIRE].

    ADS  Article  Google Scholar 

  27. T. Albash and C.V. Johnson, Vortex and droplet engineering in holographic superconductors, Phys. Rev. D 80 (2009) 126009 [arXiv:0906.1795] [INSPIRE].

    ADS  Google Scholar 

  28. M. Montull, A. Pomarol and P.J. Silva, The holographic superconductor vortex, Phys. Rev. Lett. 103 (2009) 091601 [arXiv:0906.2396] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  29. D. Roychowdhury, Vortices and supercurrent in AdS Born-Infeld gravity, arXiv:1403.0085 [INSPIRE].

  30. N. Banerjee, S. Dutta and D. Roychowdhury, Chern-Simons superconductor, arXiv:1311.7640 [INSPIRE].

  31. M. Cyrot, Ginzburg-Landau theory for superconductors, Rep. Prog. Phys. 36 (1973) 103.

    ADS  Article  Google Scholar 

  32. M. Tinkham, Introduction to superconductivity, 2nd edition, Dover, New York U.S.A. (1996).

    Google Scholar 

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

    ADS  MathSciNet  Article  MATH  Google Scholar 

  34. M. Reuter, A mechanism generating axion hair for Kerr black holes, Class. Quant. Grav. 9 (1992) 751 [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  35. M.J. Duncan, N. Kaloper and K.A. Olive, Axion hair and dynamical torsion from anomalies, Nucl. Phys. B 387 (1992) 215 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  36. G. Clement and D. Gal’tsov, Bertotti-Robinson type solutions to dilaton-axion gravity, Phys. Rev. D 63 (2001) 124011 [gr-qc/0102025] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  37. R. Li and J.-R. Ren, Holographic dual of linear dilaton black hole in Einstein-Maxwell-dilaton-axion gravity, JHEP 09 (2010) 039 [arXiv:1009.3139] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  38. M. Smolic, Holography and hydrodynamics for EMD theory with two Maxwell fields, JHEP 03 (2013) 124 [arXiv:1301.6020] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  39. J. Sonner and P.K. Townsend, Axion-dilaton domain walls and fake supergravity, Class. Quant. Grav. 24 (2007) 3479 [hep-th/0703276] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  40. J.-P. Derendinger, P.M. Petropoulos and N. Prezas, Axionic symmetry gaugings in N =4 supergravities and their higher-dimensional origin, Nucl. Phys. B 785 (2007) 115 [arXiv:0705.0008] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  41. S. Dubovsky, A. Lawrence and M.M. Roberts, Axion monodromy in a model of holographic gluodynamics, JHEP 02 (2012) 053 [arXiv:1105.3740] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  42. H. Baer, A.D. Box and H. Summy, Mainly axion cold dark matter in the minimal supergravity model, JHEP 08 (2009) 080 [arXiv:0906.2595] [INSPIRE].

    ADS  Article  Google Scholar 

  43. H. Baer and A.D. Box, Fine-tuning favors mixed axion/axino cold dark matter over neutralinos in the minimal supergravity model, Eur. Phys. J. C 68 (2010) 523 [arXiv:0910.0333] [INSPIRE].

    ADS  Article  Google Scholar 

  44. G. Tallarita and S. Thomas, Maxwell-Chern-Simons vortices and holographic superconductors, JHEP 12 (2010) 090 [arXiv:1007.4163] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

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

    ADS  Article  MATH  Google Scholar 

  46. K. Maeda and T. Okamura, Characteristic length of an AdS/CFT superconductor, Phys. Rev. D 78 (2008) 106006 [arXiv:0809.3079] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  47. H.-B. Zeng, Z.-Y. Fan and H.-S. Zong, Characteristic length of a holographic superconductor with d-wave gap, Phys. Rev. D 82 (2010) 126014 [arXiv:1006.5483] [INSPIRE].

    ADS  Google Scholar 

  48. H.-B. Zeng, Z.-Y. Fan and H.-S. Zong, Superconducting coherence length and magnetic penetration depth of a p-wave holographic superconductor, Phys. Rev. D 81 (2010) 106001 [arXiv:0912.4928] [INSPIRE].

    ADS  Google Scholar 

  49. G.V. Dunne, Aspects of Chern-Simons theory, hep-th/9902115 [INSPIRE].

  50. P.A. Horvathy, Lectures on (abelian) Chern-Simons vortices, arXiv:0704.3220 [INSPIRE].

  51. P.A. Horvathy and P. Zhang, Vortices in (abelian) Chern-Simons gauge theory, Phys. Rept. 481 (2009) 83 [arXiv:0811.2094] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dibakar Roychowdhury.

Additional information

ArXiv ePrint: 1407.3464

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Roychowdhury, D. Chern-Simons vortices and holography. J. High Energ. Phys. 2014, 18 (2014). https://doi.org/10.1007/JHEP10(2014)018

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP10(2014)018

Keywords

  • Gauge-gravity correspondence
  • Holography and condensed matter physics (AdS/CMT)
  • Black Holes