Abstract
We construct superfluid black hole solutions with two chemical potentials. By analogy with QCD, the two chemical potentials correspond to the baryon and isospin symmetries, respectively. We consider two systems: the back-reacted U(2) Einstein-Yang-Mills theory in 4 + 1 dimensions and the 9 + 1-dimensional D3/D7 brane setup with two coincident D7-brane probes. In the D7-brane model, the identification of baryon and isospin chemical potential is explicit since the dual field theory is explicitly known. Studying the phase diagram, we find in both systems a quantum phase transition at a critical ratio of the two chemical potentials. However the quantum phase transition is different in the two systems: in the D3/D7 brane setup we always find a second order phase transition, while in the Einstein-Yang-Mills theory, depending on the strength of the back-reaction, we obtain a continuous or first order transition. We expect the continuous quantum phase transition to be BKT-like. We comment on the origin of this differing behavior in these apparently very similar models and compare to phenomenological systems.
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References
S. Sachdev, Quantum phase transitions, Cambridge University Press, Cambridge U.K. (1999).
S. Sachdev, Where is the quantum critical point in the cuprate superconductors?, arXiv: 0907.0008 [SPIRES].
S. Sachdev, Condensed matter and AdS/CFT, arXiv: 1002.2947 [SPIRES].
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] [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].
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv: 0903.3246] [SPIRES].
C.P. Herzog, Lectures on holographic superuidity and superconductivity, J. Phys. A 42 (2009) 343001 [arXiv: 0904.1975] [SPIRES].
J. McGreevy, Holographic duality with a view toward many-body physics, Adv. High Energy Phys. 2010 (2010) 723105 [arXiv: 0909.0518] [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].
H. Liu, J. McGreevy and D. Vegh, Non-Fermi liquids from holography, Phys. Rev. D 83 (2011) 065029 [arXiv: 0903.2477] [SPIRES].
T. Faulkner, G.T. Horowitz and M.M. Roberts, Holographic quantum criticality from multi-trace deformations, JHEP 04 (2011) 051 [arXiv: 1008.1581] [SPIRES].
Y.-i. Shin, C.H. Schunck, A. Schirotzek and W. Ketterle, Phase diagram of a two-component Fermi gas with resonant interactions, Nature 451 (2008) 689 [arXiv: 0709.3027].
L.-y. He, M. Jin and P.-f. Zhuang, Pion superuidity and meson properties at finite isospin density, Phys. Rev. D 71 (2005) 116001 [hep-ph/0503272] [SPIRES].
M.N. Chernodub and A.S. Nedelin, Phase diagram of chirally imbalanced QCD matter, Phys. Rev. D 83 (2011) 105008 [arXiv: 1102.0188] [SPIRES].
S.S. Gubser, Colorful horizons with charge in anti-de Sitter space, Phys. Rev. Lett. 101 (2008) 191601 [arXiv: 0803.3483] [SPIRES].
S.S. Gubser and S.S. Pufu, The gravity dual of a p-wave superconductor, JHEP 11 (2008) 033 [arXiv: 0805.2960] [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 superuids with back-reaction, Phys. Lett. B 686 (2010) 192 [arXiv: 0912.3515] [SPIRES].
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] [SPIRES].
P. Basu, J. He, A. Mukherjee and H.-H. Shieh, Superconductivity from D3/D7: holographic pion superuid, JHEP 11 (2009) 070 [arXiv: 0810.3970] [SPIRES].
M. Ammon, J. Erdmenger, M. Kaminski and P. Kerner, Flavor superconductivity from gauge/gravity duality, JHEP 10 (2009) 067 [arXiv: 0903.1864] [SPIRES].
A. Karch and E. Katz, Adding avor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [SPIRES].
J. Erdmenger, N. Evans, I. Kirsch and E. Threlfall, Mesons in gauge/gravity duals — a review, Eur. Phys. J. A 35 (2008) 81 [arXiv: 0711.4467] [SPIRES].
J. Erdmenger, M. Kaminski, P. Kerner and F. Rust, Finite baryon and isospin chemical potential in AdS/CFT with flavor, JHEP 11 (2008) 031 [arXiv: 0807.2663] [SPIRES].
D.B. Kaplan, J.-W. Lee, D.T. Son and M.A. Stephanov, Conformality lost, Phys. Rev. D 80 (2009) 125005 [arXiv: 0905.4752] [SPIRES].
V.G. Filev, C.V. Johnson, R.C. Rashkov and K.S. Viswanathan, Flavoured large-N gauge theory in an external magnetic field, JHEP 10 (2007) 019 [hep-th/0701001] [SPIRES].
J. Erdmenger, R. Meyer and J.P. Shock, AdS/CFT with flavour in electric and magnetic Kalb-Ramond fields, JHEP 12 (2007) 091 [arXiv: 0709.1551] [SPIRES].
N. Evans, A. Gebauer, K.-Y. Kim and M. Magou, Phase diagram of the D3/D5 system in a magnetic field and a BKT transition, Phys. Lett. B 698 (2011) 91 [arXiv: 1003.2694] [SPIRES].
N. Evans, A. Gebauer, K.-Y. Kim and M. Magou, Holographic description of the phase diagram of a chiral symmetry breaking gauge theory, JHEP 03 (2010) 132 [arXiv: 1002.1885] [SPIRES].
K. Jensen, A. Karch, D.T. Son and E.G. Thompson, Holographic Berezinskii-Kosterlitz-Thouless transitions, Phys. Rev. Lett. 105 (2010) 041601 [arXiv: 1002.3159] [SPIRES].
S.S. Pal, Quantum phase transition in a Dp-Dq system, Phys. Rev. D 82 (2010) 086013 [arXiv: 1006.2444] [SPIRES].
K. Jensen, More holographic Berezinskii-Kosterlitz-Thouless transitions, Phys. Rev. D 82 (2010) 046005 [arXiv: 1006.3066] [SPIRES].
N. Evans, K. Jensen and K.-Y. Kim, Non mean-field quantum critical points from holography, Phys. Rev. D 82 (2010) 105012 [arXiv: 1008.1889] [SPIRES].
R. Manvelyan, E. Radu and D.H. Tchrakian, New AdS non Abelian black holes with superconducting horizons, Phys. Lett. B 677 (2009) 79 [arXiv: 0812.3531] [SPIRES].
S. Kobayashi, D. Mateos, S. Matsuura, R.C. Myers and R.M. Thomson, Holographic phase transitions at finite baryon density, JHEP 02 (2007) 016 [hep-th/0611099] [SPIRES].
V. Balasubramanian and P. Kraus, A stress tensor for anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [SPIRES].
S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of spacetime and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [SPIRES].
N. Iqbal, H. Liu, M. Mezei and Q. Si, Quantum phase transitions in holographic models of magnetism and superconductors, Phys. Rev. D 82 (2010) 045002 [arXiv: 1003.0010] [SPIRES].
G.T. Horowitz and M.M. Roberts, Zero temperature limit of holographic superconductors, JHEP 11 (2009) 015 [arXiv: 0908.3677] [SPIRES].
C.P. Herzog and S.S. Pufu, The second sound of SU(2), JHEP 04 (2009) 126 [arXiv: 0902.0409] [SPIRES].
C.P. Herzog, An analytic holographic superconductor, Phys. Rev. D 81 (2010) 126009 [arXiv: 1003.3278] [SPIRES].
R.C. Myers, Dielectric-branes, JHEP 12 (1999) 022 [hep-th/9910053] [SPIRES].
A.A. Tseytlin, On non-Abelian generalisation of the Born-Infeld action in string theory, Nucl. Phys. B 501 (1997) 41 [hep-th/9701125] [SPIRES].
A. Hashimoto and W. Taylor, Fluctuation spectra of tilted and intersecting D-branes from the Born-Infeld action, Nucl. Phys. B 503 (1997) 193 [hep-th/9703217] [SPIRES].
N.R. Constable, R.C. Myers and O. Tafjord, The noncommutative bion core, Phys. Rev. D 61 (2000) 106009 [hep-th/9911136] [SPIRES].
R.C. Myers and M.C. Wapler, Transport properties of holographic defects, JHEP 12 (2008) 115 [arXiv: 0811.0480] [SPIRES].
A. Karch and A. O’Bannon, Holographic thermodynamics at finite baryon density: some exact results, JHEP 11 (2007) 074 [arXiv: 0709.0570] [SPIRES].
D. Mateos, S. Matsuura, R.C. Myers and R.M. Thomson, Holographic phase transitions at finite chemical potential, JHEP 11 (2007) 085 [arXiv: 0709.1225] [SPIRES].
K. Skenderis, Lecture notes on holographic renormalization, Class. Quant. Grav. 19 (2002) 5849 [hep-th/0209067] [SPIRES].
A. Karch, A. O’Bannon and K. Skenderis, Holographic renormalization of probe D-branes in AdS/CFT, JHEP 04 (2006) 015 [hep-th/0512125] [SPIRES].
D. Mateos, R.C. Myers and R.M. Thomson, Thermodynamics of the brane, JHEP 05 (2007) 067 [hep-th/0701132] [SPIRES].
J. Erdmenger, M. Kaminski and F. Rust, Holographic vector mesons from spectral functions at finite baryon or isospin density, Phys. Rev. D 77 (2008) 046005 [arXiv: 0710.0334] [SPIRES].
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ArXiv ePrint: 1103.4145
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Erdmenger, J., Grass, V., Kerner, P. et al. Holographic superuidity in imbalanced mixtures. J. High Energ. Phys. 2011, 37 (2011). https://doi.org/10.1007/JHEP08(2011)037
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DOI: https://doi.org/10.1007/JHEP08(2011)037