Abstract
In the current work we study various models of holographic superconductors at low temperature. Generically the zero temperature limit of those models are solitonic solution with a zero sized horizon. Here we generalized simple version of those zero temperature solutions to small but non-zero temperature T. We confine ourselves to cases where near horizon geometry is AdS 4. At a non-zero temperature a small horizon would form deep inside this AdS 4 which does not disturb the UV physics. The resulting geometry may be matched with the zero temperature solution at an intermediate length scale. We understand this matching from separation of scales by setting up a perturbative expansion in gauge potential. We have a better analytic control in abelian case and quantities may be expressed in terms of hypergeometric function. From this we calculate low temperature behavior of various quatities like entropy, charge density and specific heat etc. We also calculate various energy gaps associated with p-wave holographic superconductor to understand the underlying pairing mechanism. The result deviates significantly from the corresponding weak coupling BCS counterpart.
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References
S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [SPIRES].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a holographic superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [SPIRES].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [SPIRES].
S.S. Gubser and S.S. Pufu, The gravity dual of a p-wave superconductor, JHEP 11 (2008) 033 [arXiv:0805.2960] [SPIRES].
S.S. Gubser, Colorful horizons with charge in Anti-de Sitter space, Phys. Rev. Lett. 101 (2008) 191601 [arXiv:0803.3483] [SPIRES].
M.M. Roberts and S.A. Hartnoll, Pseudogap and time reversal breaking in a holographic superconductor, JHEP 08 (2008) 035 [arXiv:0805.3898] [SPIRES].
G.T. Horowitz and M.M. Roberts, Zero temperature limit of holographic superconductors, JHEP 11 (2009) 015 [arXiv:0908.3677] [SPIRES].
S.S. Gubser and A. Nellore, Ground states of holographic superconductors, Phys. Rev. D 80 (2009) 105007 [arXiv:0908.1972] [SPIRES].
S.S. Gubser, S.S. Pufu and F.D. Rocha, Quantum critical superconductors in string theory and M-theory, Phys. Lett. B 683 (2010) 201 [arXiv:0908.0011] [SPIRES].
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] [SPIRES].
J.P. Gauntlett, J. Sonner and T. Wiseman, Holographic superconductivity in M-theory, Phys. Rev. Lett. 103 (2009) 151601 [arXiv:0907.3796] [SPIRES].
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].
R.A. Konoplya and A. Zhidenko, Holographic conductivity of zero temperature superconductors, Phys. Lett. B 686 (2010) 199 [arXiv:0909.2138] [SPIRES].
P. Basu, J. He, A. Mukherjee and H.-H. Shieh, Hard-gapped Holographic superconductors, Phys. Lett. B 689 (2010) 45 [arXiv:0911.4999] [SPIRES].
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] [SPIRES].
C.P. Herzog and S.S. Pufu, The second sound of SU(2), JHEP 04 (2009) 126 [arXiv:0902.0409] [SPIRES].
J.-W. Chen, Y.-J. Kao and W.-Y. Wen, Peak-dip-hump from holographic superconductivity, Phys. Rev. D 82 (2010) 026007 [arXiv:0911.2821] [SPIRES].
S.S. Gubser, F.D. Rocha and P. Talavera, Normalizable fermion modes in a holographic superconductor, JHEP 10 (2010) 087 [arXiv:0911.3632] [SPIRES].
M. Ammon, J. Erdmenger, M. Kaminski and A. O’Bannon, Fermionic operator mixing in holographic p-wave superfluids, JHEP 05 (2010) 053 [arXiv:1003.1134] [SPIRES].
S.S. Gubser, F.D. Rocha and A. Yarom, Fermion correlators in non-abelian holographic superconductors, JHEP 11 (2010) 085 [arXiv:1002.4416] [SPIRES].
T. Faulkner, G.T. Horowitz, J. McGreevy, M.M. Roberts and D. Vegh, Photoemission ’experiments’ on holographic superconductors, JHEP 03 (2010) 121 [arXiv:0911.3402] [SPIRES].
J. Erdmenger, P. Kerner and H. Zeller, Non-universal shear viscosity from Einstein gravity, arXiv:1011.5912 [SPIRES].
M. Natsuume and M. Ohta, The shear viscosity of holographic superfluids, Prog. Theor. Phys. 124 (2010) 931 [arXiv:1008.4142] [SPIRES].
K. Peeters, J. Powell and M. Zamaklar, Exploring colourful holographic superconductors, JHEP 09 (2009) 101 [arXiv:0907.1508] [SPIRES].
P. Basu, A. Mukherjee and H.-H. Shieh, Supercurrent: vector hair for an AdS Black Hole, Phys. Rev. D 79 (2009) 045010 [arXiv:0809.4494] [SPIRES].
C.P. Herzog, P.K. Kovtun and D.T. Son, Holographic model of superfluidity, Phys. Rev. D 79 (2009) 066002 [arXiv:0809.4870] [SPIRES].
P. Basu, J. He, A. Mukherjee and H.-H. Shieh, Superconductivity from D3/D7: holographic pion superfluid, JHEP 11 (2009) 070 [arXiv:0810.3970] [SPIRES].
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ArXiv ePrint: 1101.0215
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Basu, P. Low temperature properties of holographic condensates. J. High Energ. Phys. 2011, 142 (2011). https://doi.org/10.1007/JHEP03(2011)142
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DOI: https://doi.org/10.1007/JHEP03(2011)142