Abstract
We have studied holographic superconductors with spherical symmetry in the Hořava-Lifshitz gravity by using a semi analytical method, and also we have calculated the critical temperature and shown when the condensation will appear in a similar pattern as in the Einstein-Gauss-Bonnet gravity. We have computed the dependency of the conductivity as a function of frequency in this new non-relativistic model of quantum gravity.
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S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a holographic superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [SPIRES].
P. Breitenlohner and D.Z. Freedman, Stability in gauged extended supergravity, Ann. Phys. 144 (1982) 249 [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].
W.-Y. Wen, Inhomogeneous magnetic field in AdS/CFT superconductor, arXiv:0805.1550 [SPIRES].
S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [SPIRES].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].
K. Maeda and T. Okamura, Characteristic length of an AdS/CFT superconductor, Phys. Rev. D 78 (2008) 106006 [arXiv:0809.3079] [SPIRES].
E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [SPIRES].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [SPIRES].
P. Hořava, Quantum criticality and Yang-Mills gauge theory, Phys. Lett. B 694 (2010) 172 [arXiv:0811.2217] [SPIRES].
P. Hořava, Membranes at quantum criticality, JHEP 03 (2009) 020 [arXiv:0812.4287] [SPIRES].
P. Hořava, Quantum gravity at a Lifshitz point, Phys. Rev. D 79 (2009) 084008 [arXiv:0901.3775] [SPIRES].
P. Hořava, Spectral dimension of the universe in quantum gravity at a Lifshitz point, Phys. Rev. Lett. 102 (2009) 161301 [arXiv:0902.3657] [SPIRES].
D. Blas, O. Pujolàs and S. Sibiryakov, On the extra mode and inconsistency of Hořava gravity, JHEP 10 (2009) 029 [arXiv:0906.3046] [SPIRES].
A. Kehagias and K. Sfetsos, The black hole and FRW geometries of non-relativistic gravity, Phys. Lett. B 678 (2009) 123 [arXiv:0905.0477] [SPIRES].
M.R. Setare and D. Momeni, Geodesic stability for KS black hole in Hořava-Lifshitz gravity via Lyapunov exponents, Int. J. Theor. Phys. 50 (2011) 106 [arXiv:1001.3767] [SPIRES].
H. Lü, J. Mei and C.N. Pope, Solutions to Hořava gravity, Phys. Rev. Lett. 103 (2009) 091301 [arXiv:0904.1595] [SPIRES].
J.-Z. Tang, Static charged black hole solutions in Hořava-Lifshitz gravity, arXiv:0911.3849 [SPIRES].
R.-G. Cai, L.-M. Cao and N. Ohta, Topological black holes in Hořava-Lifshitz gravity, Phys. Rev. D 80 (2009) 024003 [arXiv:0904.3670] [SPIRES].
X.-H. Ge, B. Wang, S.-F. Wu and G.-H. Yang, Analytical study on holographic superconductors in external magnetic field, JHEP 08 (2010) 108 [arXiv:1002.4901] [SPIRES].
Q. Pan, B. Wang, E. Papantonopoulos, J. Oliveira and A.B. Pavan, Holographic superconductors with various condensates in Einstein-Gauss-Bonnet gravity, Phys. Rev. D 81 (2010) 106007 [arXiv:0912.2475] [SPIRES].
Y. Liu, Q. Pan, B. Wang and R.-G. Cai, Dynamical perturbations and critical phenomena in Gauss-Bonnet-AdS black holes, Phys. Lett. B 693 (2010) 343 [arXiv:1007.2536] [SPIRES].
Q. Pan and B. Wang, General holographic superconductor models with backreactions, arXiv:1101.0222 [SPIRES].
Q. Pan and B. Wang, General holographic superconductor models with Gauss-Bonnet corrections, Phys. Lett. B 693 (2010) 159 [arXiv:1005.4743] [SPIRES].
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] [SPIRES].
J. Jing, L. Wang and S. Chen, Holographic superconductors in z = 3 Hořava-Lifshitz gravity without condition of detailed balance, arXiv:1001.1472 [SPIRES].
R.L. Arnowitt, S. Deser and C.W. Misner, The dynamics of general relativity, in Gravitation: an introduction to current research, L. Witten ed., John Wiley and Sons Inc., New York U.S.A. (1962) [gr-qc/0405109] [SPIRES].
T.P. Sotiriou, M. Visser and S. Weinfurtner, Phenomenologically viable Lorentz-violating quantum gravity, Phys. Rev. Lett. 102 (2009) 251601 [arXiv:0904.4464] [SPIRES].
T.P. Sotiriou, M. Visser and S. Weinfurtner, Quantum gravity without Lorentz invariance, JHEP 10 (2009) 033 [arXiv:0905.2798] [SPIRES].
G.W. Gibbons and S.W. Hawking, Classification of gravitational instanton symmetries, Commun. Math. Phys. 66 (1979) 291 [SPIRES].
R.A. Konoplya, Entropic force, holography and thermodynamics for static space-times, Eur. Phys. J. C 69 (2010) 555 [arXiv:1002.2818] [SPIRES].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [SPIRES].
L.J. Romans, Supersymmetric, cold and lukewarm black holes in cosmological Einstein-Maxwell theory, Nucl. Phys. B 383 (1992) 395 [hep-th/9203018] [SPIRES].
T. Albash and C.V. Johnson, A holographic superconductor in an external magnetic field, JHEP 09 (2008) 121 [arXiv:0804.3466] [SPIRES].
R.-G. Cai and H.-Q. Zhang, Holographic superconductors with Hořava-Lifshitz black holes, Phys. Rev. D 81 (2010) 066003 [arXiv:0911.4867] [SPIRES].
P. Kanti and J. March-Russell, Calculable corrections to brane black hole decay. II: Greybody factors for spin 1/2 and 1, Phys. Rev. D 67 (2003) 104019 [hep-ph/0212199] [SPIRES].
I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [SPIRES].
R. Gregory, S. Kanno and J. Soda, Holographic superconductors with higher curvature corrections, JHEP 10 (2009) 010 [arXiv:0907.3203] [SPIRES].
R. Gregory, Holographic superconductivity with Gauss-Bonnet gravity, J. Phys. Conf. Ser. 283 (2011) 012016 [arXiv:1012.1558] [SPIRES].
L. Barclay, R. Gregory, S. Kanno and P. Sutcliffe, Gauss-Bonnet holographic superconductors, JHEP 12 (2010) 029 [arXiv:1009.1991] [SPIRES].
G.T. Horowitz and M.M. Roberts, Holographic superconductors with various condensates, Phys. Rev. D 78 (2008) 126008 [arXiv:0810.1077] [SPIRES].
K. Skenderis, Lecture notes on holographic renormalization, Class. Quant. Grav. 19 (2002) 5849 [hep-th/0209067] [SPIRES].
D.T. Son and A.O. Starinets, Minkowski-space correlators in AdS/CFT correspondence: recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [SPIRES].
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ArXiv ePrint: 1003.0376
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Momeni, D., Setare, M.R. & Majd, N. Holographic superconductors in a model of non-relativistic gravity. J. High Energ. Phys. 2011, 118 (2011). https://doi.org/10.1007/JHEP05(2011)118
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DOI: https://doi.org/10.1007/JHEP05(2011)118