Abstract
In the present paper, based on the notion of marginally stable modes of vector perturbations in the AdS soliton back ground we investigate the magnetic field effect on holographic p-wave insulator/superconductor transition in the probe limit. We perform explicit analytic calculations considering both Schwarzschild AdS soliton and Gauss Bonnet AdS soliton back grounds and obtain a unique relation between the chemical potential and the magnetic field near the critical point. We also extend our analysis for p + ip-wave back ground in the presence of external magnetic field. In both the cases it is observed that the non abelian model exhibit droplet solutions. Moreover it is also found that the increase in the value of the external magnetic field essentially reduces the size of the droplet and thereby makes the condensation harder.
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J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
G.T. Horowitz and J. Polchinski, Gauge/gravity duality, gr-qc/0602037 [INSPIRE].
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].
C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].
G.T. Horowitz, Theory of Superconductivity, Lect. Notes Phys. 828 (2011) 313 [arXiv:1002.1722] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].
S.S. Gubser, Phase transitions near black hole horizons, Class. Quant. Grav. 22 (2005) 5121 [hep-th/0505189] [INSPIRE].
S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [INSPIRE].
S.S. Gubser, Colorful horizons with charge in anti-de Sitter space, Phys. Rev. Lett. 101 (2008) 191601 [arXiv:0803.3483] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].
G.T. Horowitz and M.M. Roberts, Holographic Superconductors with Various Condensates, Phys. Rev. D 78 (2008) 126008 [arXiv:0810.1077] [INSPIRE].
G.T. Horowitz and M.M. Roberts, Zero Temperature Limit of Holographic Superconductors, JHEP 11 (2009) 015 [arXiv:0908.3677] [INSPIRE].
G. Siopsis and J. Therrien, Analytic Calculation of Properties of Holographic Superconductors, JHEP 05 (2010) 013 [arXiv:1003.4275] [INSPIRE].
R. Gregory, S. Kanno and J. Soda, Holographic Superconductors with Higher Curvature Corrections, JHEP 10 (2009) 010 [arXiv:0907.3203] [INSPIRE].
P. Basu, J. He, A. Mukherjee and H.-H. Shieh, Hard-gapped Holographic Superconductors, Phys. Lett. B 689 (2010) 45 [arXiv:0911.4999] [INSPIRE].
H.-B. Zeng, W.-M. Sun and H.-S. Zong, Supercurrent in p-wave Holographic Superconductor, Phys. Rev. D 83 (2011) 046010 [arXiv:1010.5039] [INSPIRE].
F. Aprile, D. Rodriguez-Gomez and J.G. Russo, p-wave Holographic Superconductors and five-dimensional gauged Supergravity, JHEP 01 (2011) 056 [arXiv:1011.2172] [INSPIRE].
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].
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].
S.S. Gubser and S.S. Pufu, The Gravity dual of a p-wave superconductor, JHEP 11 (2008) 033 [arXiv:0805.2960] [INSPIRE].
R. Manvelyan, E. Radu and D. Tchrakian, New AdS non Abelian black holes with superconducting horizons, Phys. Lett. B 677 (2009) 79 [arXiv:0812.3531] [INSPIRE].
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].
R.-G. Cai, Z.-Y. Nie and H.-Q. Zhang, Holographic p-wave superconductors from Gauss-Bonnet gravity, Phys. Rev. D 82 (2010) 066007 [arXiv:1007.3321] [INSPIRE].
Q. Pan and B. Wang, General holographic superconductor models with Gauss-Bonnet corrections, Phys. Lett. B 693 (2010) 159 [arXiv:1005.4743] [INSPIRE].
M.M. Roberts and S.A. Hartnoll, Pseudogap and time reversal breaking in a holographic superconductor, JHEP 08 (2008) 035 [arXiv:0805.3898] [INSPIRE].
G.T. Horowitz, J.E. Santos and B. Way, A Holographic Josephson Junction, Phys. Rev. Lett. 106 (2011) 221601 [arXiv:1101.3326] [INSPIRE].
S. Gangopadhyay and D. Roychowdhury, Analytic study of properties of holographic superconductors in Born-Infeld electrodynamics, JHEP 05 (2012) 002 [arXiv:1201.6520] [INSPIRE].
S. Gangopadhyay and D. Roychowdhury, Analytic study of Gauss-Bonnet holographic superconductors in Born-Infeld electrodynamics, JHEP 05 (2012) 156 [arXiv:1204.0673] [INSPIRE].
S. Gangopadhyay and D. Roychowdhury, Analytic study of properties of holographic p-wave superconductors, JHEP 08 (2012) 104 [arXiv:1207.5605] [INSPIRE].
R. Banerjee, S. Gangopadhyay, D. Roychowdhury and A. Lala, Holographic s-wave condensate with non-linear electrodynamics: A nontrivial boundary value problem, Phys. Rev. D 87 (2013) 104001 [arXiv:1208.5902] [INSPIRE].
D. Roychowdhury, AdS/CFT superconductors with Power Maxwell electrodynamics: reminiscent of the Meissner effect, Phys. Lett. B 718 (2013) 1089 [arXiv:1211.1612] [INSPIRE].
D. Roychowdhury, Effect of external magnetic field on holographic superconductors in presence of nonlinear corrections, Phys. Rev. D 86 (2012) 106009 [arXiv:1211.0904] [INSPIRE].
K. Maeda, M. Natsuume and T. Okamura, Vortex lattice for a holographic superconductor, Phys. Rev. D 81 (2010) 026002 [arXiv:0910.4475] [INSPIRE].
M. Montull, A. Pomarol and P.J. Silva, The Holographic Superconductor Vortex, Phys. Rev. Lett. 103 (2009) 091601 [arXiv:0906.2396] [INSPIRE].
T. Albash and C.V. Johnson, A Holographic Superconductor in an External Magnetic Field, JHEP 09 (2008) 121 [arXiv:0804.3466] [INSPIRE].
T. Albash and C.V. Johnson, Vortex and Droplet Engineering in Holographic Superconductors, Phys. Rev. D 80 (2009) 126009 [arXiv:0906.1795] [INSPIRE].
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] [INSPIRE].
A. Salvio, Holographic Superfluids and Superconductors in Dilaton-Gravity, JHEP 09 (2012) 134 [arXiv:1207.3800] [INSPIRE].
O. Domenech, M. Montull, A. Pomarol, A. Salvio and P.J. Silva, Emergent Gauge Fields in Holographic Superconductors, JHEP 08 (2010) 033 [arXiv:1005.1776] [INSPIRE].
H.-B. Zeng, Z.-Y. Fan and H.-S. Zong, d-wave Holographic Superconductor Vortex Lattice and Non-Abelian Holographic Superconductor Droplet, Phys. Rev. D 82 (2010) 126008 [arXiv:1007.4151] [INSPIRE].
B.S. Acharya and M. Torabian, Supersymmetry Breaking, Moduli Stabilization and Hidden U(1) Breaking in M-theory, Phys. Rev. D 83 (2011) 126001 [arXiv:1101.0108] [INSPIRE].
D. Gao, Vortex and droplet in holographic D-wave superconductors, Phys. Lett. A 376 (2012) 1705 [arXiv:1112.2422] [INSPIRE].
T. Nishioka, S. Ryu and T. Takayanagi, Holographic Superconductor/Insulator Transition at Zero Temperature, JHEP 03 (2010) 131 [arXiv:0911.0962] [INSPIRE].
G.T. Horowitz and R.C. Myers, The AdS/CFT correspondence and a new positive energy conjecture for general relativity, Phys. Rev. D 59 (1998) 026005 [hep-th/9808079] [INSPIRE].
E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].
S. Surya, K. Schleich and D.M. Witt, Phase transitions for flat AdS black holes, Phys. Rev. Lett. 86 (2001) 5231 [hep-th/0101134] [INSPIRE].
G.T. Horowitz and B. Way, Complete Phase Diagrams for a Holographic Superconductor/Insulator System, JHEP 11 (2010) 011 [arXiv:1007.3714] [INSPIRE].
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].
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].
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].
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].
Y.-Q. Wang, Y.-X. Liu, R.-G. Cai, S. Takeuchi and H.-Q. Zhang, Holographic SIS Josephson Junction, JHEP 09 (2012) 058 [arXiv:1205.4406] [INSPIRE].
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].
R.-G. Cai, X. He, H.-F. Li and H.-Q. Zhang, Phase transitions in AdS soliton spacetime through marginally stable modes, Phys. Rev. D 84 (2011) 046001 [arXiv:1105.5000] [INSPIRE].
Z. Zhao, Q. Pan and J. Jing, Holographic insulator/superconductor phase transition with Weyl corrections, Phys. Lett. B 719 (2013) 440 [arXiv:1212.3062] [INSPIRE].
N. Bai, Y.-H. Gao, B.-G. Qi and X.-B. Xu, Holographic insulator/superconductor phase transition in Born-Infeld electrodynamics, arXiv:1212.2721 [INSPIRE].
A. Akhavan and M. Alishahiha, P-Wave Holographic Insulator/Superconductor Phase Transition, Phys. Rev. D 83 (2011) 086003 [arXiv:1011.6158] [INSPIRE].
J. Harms, J.P. Toennies, F. Dalfovo, Density of superfluid helium droplets, Phys. Rev. B 58 (1998) 3341.
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Roychowdhury, D. Holographic droplets in p-wave insulator/superconductor transition. J. High Energ. Phys. 2013, 162 (2013). https://doi.org/10.1007/JHEP05(2013)162
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DOI: https://doi.org/10.1007/JHEP05(2013)162