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Analytical study on holographic superconductors with backreactions

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Abstract

We employ the variational method for the Sturm-Liouville eigenvalue problem to analytically investigate the properties of the holographic superconductors. We find that the analytic method is still powerful when the backreaction is turned on. Reducing step size in the iterative procedure, we observe that the consistency of results between the analytic and numerical computations can be further improved. The obtained analytic result can be used to back up the numerical computations in the holographic superconductor in the fully backreacted spacetime.

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References

  1. J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  ADS  MATH  Google Scholar 

  3. 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].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  6. 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 

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

    Article  MathSciNet  ADS  Google Scholar 

  8. C.P. Herzog, Lectures on holographic superfluidity and superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].

    Google Scholar 

  9. G.T. Horowitz, Introduction to holographic superconductors, arXiv:1002.1722 [INSPIRE].

  10. M. Ammon, J. Erdmenger, V. Grass, P. Kerner and A. O’Bannon, On holographic p-wave superfluids with back-reaction, Phys. Lett. B 686 (2010) 192 [arXiv:0912.3515] [INSPIRE].

    Article  ADS  Google Scholar 

  11. R.-G. Cai, Z.-Y. Nie and H.-Q. Zhang, Holographic phase transitions of p-wave superconductors in Gauss-Bonnet gravity with back-reaction, Phys. Rev. D 83 (2011) 066013 [arXiv:1012.5559] [INSPIRE].

    ADS  Google Scholar 

  12. S.S. Gubser and A. Nellore, Low-temperature behavior of the abelian Higgs model in Anti-de Sitter space, JHEP 04 (2009) 008 [arXiv:0810.4554] [INSPIRE].

    Article  ADS  Google Scholar 

  13. F. Aprile and J.G. Russo, Models of holographic superconductivity, Phys. Rev. D 81 (2010) 026009 [arXiv:0912.0480] [INSPIRE].

    ADS  Google Scholar 

  14. Y. Brihaye and B. Hartmann, Holographic superconductors in 3 + 1 dimensions away from the probe limit, Phys. Rev. D 81 (2010) 126008 [arXiv:1003.5130] [INSPIRE].

    ADS  Google Scholar 

  15. Y. Liu and Y.W. Sun, Holographic superconductors from Einstein-Maxwell-Dilaton gravity, JHEP 07 (2010) 099 [arXiv:1006.2726] [INSPIRE].

    Article  ADS  Google Scholar 

  16. L. Barclay, R. Gregory, S. Kanno and P. Sutcliffe, Gauss-Bonnet holographic superconductors, JHEP 12 (2010) 029 [arXiv:1009.1991] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  17. M. Siani, Holographic superconductors and higher curvature corrections, JHEP 12 (2010) 035 [arXiv:1010.0700] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  18. L. Barclay, The rich structure of Gauss-Bonnet holographic superconductors, JHEP 10 (2011) 044 [arXiv:1012.3074] [INSPIRE].

    Article  ADS  Google Scholar 

  19. Q. Pan and B. Wang, General holographic superconductor models with backreactions, arXiv:1101.0222 [INSPIRE].

  20. Y. Liu, Q. Pan and B. Wang, Holographic superconductor developed in BTZ black hole background with backreactions, Phys. Lett. B 702 (2011) 94 [arXiv:1106.4353] [INSPIRE].

    Article  ADS  Google Scholar 

  21. R. Gregory, Holographic superconductivity with Gauss-Bonnet gravity, J. Phys. Conf. Ser. 283 (2011) 012016 [arXiv:1012.1558] [INSPIRE].

    Article  ADS  Google Scholar 

  22. Y. Liu, Y. Peng and B. Wang, Gauss-Bonnet holographic superconductors in Born-Infeld electrodynamics with backreactions, arXiv:1202.3586 [INSPIRE].

  23. G.T. Horowitz and B. Way, Complete phase diagrams for a holographic superconductor/insulator system, JHEP 11 (2010) 011 [arXiv:1007.3714] [INSPIRE].

    Article  ADS  Google Scholar 

  24. Y. Peng, Q. Pan and B. Wang, Various types of phase transitions in the AdS soliton background, Phys. Lett. B 699 (2011) 383 [arXiv:1104.2478] [INSPIRE].

    Article  ADS  Google Scholar 

  25. A. Akhavan and M. Alishahiha, p-wave holographic insulator/superconductor phase transition, Phys. Rev. D 83 (2011) 086003 [arXiv:1011.6158] [INSPIRE].

    ADS  Google Scholar 

  26. Y. Brihaye and B. Hartmann, Holographic superfluid/fluid/insulator phase transitions in 2 + 1 dimensions, Phys. Rev. D 83(2011) 126008 [arXiv:1101.5708][INSPIRE].

    ADS  Google Scholar 

  27. Y. Peng, X.-M. Kuang, Y. Liu and B. Wang, Phase transition in the holographic model of superfluidity with backreactions, arXiv:1204.2853 [INSPIRE].

  28. R. Gregory, S. Kanno and J. Soda, Holographic superconductors with higher curvature corrections, JHEP 10 (2009) 010 [arXiv:0907.3203] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  29. Q. Pan, B. Wang, E. Papantonopoulos, J. Oliveira and A. Pavan, Holographic superconductors with various condensates in Einstein-Gauss-Bonnet gravity, Phys. Rev. D 81 (2010) 106007 [arXiv:0912.2475] [INSPIRE].

    ADS  Google Scholar 

  30. S. Kanno, A note on Gauss-Bonnet holographic superconductors, Class. Quant. Grav. 28 (2011) 127001 [arXiv:1103.5022] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. X.-H. Ge, Analytical calculation on critical magnetic field in holographic superconductors with backreaction, arXiv:1105.4333 [INSPIRE].

  32. G. Siopsis and J. Therrien, Analytic calculation of properties of holographic superconductors, JHEP 05 (2010) 013 [arXiv:1003.4275] [INSPIRE].

    Article  ADS  Google Scholar 

  33. G. Siopsis, J. Therrien and S. Musiri, Holographic superconductors near the Breitenlohner-Freedman bound, Class. Quant. Grav. 29 (2012) 085007 [arXiv:1011.2938] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  34. H.-B. Zeng, X. Gao, Y. Jiang and H.-S. Zong, Analytical computation of critical exponents in several holographic superconductors, JHEP 05 (2011) 002 [arXiv:1012.5564] [INSPIRE].

    Article  ADS  Google Scholar 

  35. H.-F. Li, R.-G. Cai and H.-Q. Zhang, Analytical studies on holographic superconductors in Gauss-Bonnet gravity, JHEP 04 (2011) 028 [arXiv:1103.2833] [INSPIRE].

    Article  ADS  Google Scholar 

  36. J. Jing, Q. Pan and S. Chen, Holographic superconductors with power-Maxwell field, JHEP 11 (2011) 045 [arXiv:1106.5181] [INSPIRE].

    Article  ADS  Google Scholar 

  37. D. Momeni, N. Majd and R. Myrzakulov, p-wave holographic superconductors with Weyl corrections, Europhys. Lett. 97 (2012) 61001 [arXiv:1204.1246] [INSPIRE].

    Article  ADS  Google Scholar 

  38. J.A. Hutasoit, S. Ganguli, G. Siopsis and J. Therrien, Strongly coupled striped superconductor with large modulation, JHEP 02 (2012) 086 [arXiv:1110.4632] [INSPIRE].

    Article  ADS  Google Scholar 

  39. S. Gangopadhyay and D. Roychowdhury, Analytic study of properties of holographic superconductors in Born-Infeld electrodynamics, JHEP 05 (2012) 002 [arXiv:1201.6520] [INSPIRE].

    Article  ADS  Google Scholar 

  40. S. Gangopadhyay and D. Roychowdhury, Analytic study of Gauss-Bonnet holographic superconductors in Born-Infeld electrodynamics, JHEP 05 (2012) 156 [arXiv:1204.0673] [INSPIRE].

    Article  ADS  Google Scholar 

  41. S. Ganguli, J.A. Hutasoit and G. Siopsis, Enhancement of critical temperature of a striped holographic superconductor, arXiv:1205.3107 [INSPIRE].

  42. R.-G. Cai, H.-F. Li and H.-Q. Zhang, Analytical studies on holographic insulator/superconductor phase transitions, Phys. Rev. D 83 (2011) 126007 [arXiv:1103.5568] [INSPIRE].

    ADS  Google Scholar 

  43. R.-G. Cai, L. Li, H.-Q. Zhang and Y.-L. Zhang, Magnetic field effect on the phase transition in AdS soliton spacetime, Phys. Rev. D 84 (2011) 126008 [arXiv:1109.5885] [INSPIRE].

    ADS  Google Scholar 

  44. Q. Pan, J. Jing and B. Wang, Analytical investigation of the phase transition between holographic insulator and superconductor in Gauss-Bonnet gravity, JHEP 11 (2011) 088 [arXiv:1105.6153] [INSPIRE].

    Article  ADS  Google Scholar 

  45. C.O. Lee, The holographic superconductors in higher-dimensional AdS soliton, arXiv:1202.5146 [INSPIRE].

  46. C.P. Herzog, An analytic holographic superconductor, Phys. Rev. D 81 (2010) 126009 [arXiv:1003.3278] [INSPIRE].

    ADS  Google Scholar 

  47. I.M. Gelfand and S.V. Fomin, Calculaus of variations, revised English edition, Prentice-Hall, Englewood Cliff, U.S.A. (1963).

  48. G.T. Horowitz and M.M. Roberts, Holographic superconductors with various condensates, Phys. Rev. D 78 (2008) 126008 [arXiv:0810.1077] [INSPIRE].

    ADS  Google Scholar 

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Authors and Affiliations

  1. Institute of Physics and Department of Physics, Hunan Normal University, Changsha, Hunan, 410081, P.R. China

    Qiyuan Pan, Jiliang Jing & Songbai Chen

  2. Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha, Hunan, 410081, P.R. China

    Qiyuan Pan, Jiliang Jing & Songbai Chen

  3. INPAC, Department of Physics and Shanghai Key Lab for Particle Physics and Cosmology, Shanghai Jiao Tong University, Shanghai, 200240, P.R. China

    Bin Wang

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  1. Qiyuan Pan
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Correspondence to Qiyuan Pan.

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Pan, Q., Jing, J., Wang, B. et al. Analytical study on holographic superconductors with backreactions. J. High Energ. Phys. 2012, 87 (2012). https://doi.org/10.1007/JHEP06(2012)087

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