Abstract
We analyse the infinite class of d = 3 CFTs dual to skew-whiffed AdS 4 × SE 7 solutions of D = 11 supergravity at finite temperature and charge density and in the presence of a magnetic field. We construct black hole solutions corresponding to the unbroken phase, and at zero temperature some of these become dyonic domain walls of an Einstein-Maxwell-pseudo-scalar theory interpolating between AdS 4 in the UV and new families of dyonic \( Ad{S_2}\times {{\mathbb{R}}^2} \) solutions in the IR. The black holes exhibit both diamagnetic and paramagnetic behaviour. We analyse superfluid and striped instabilities and show that for large enough values of the magnetic field the superfluid instability disappears while the striped instability remains. For larger values of the magnetic field there is also a first-order metamagnetic phase transition and at zero temperature these black hole solutions exhibit hyperscaling violation in the IR with dynamical exponent z = 3/2 and θ = −2.
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S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008)065034 [arXiv:0801.2977] [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.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008)015 [arXiv:0810.1563] [INSPIRE].
J.P. Gauntlett, J. Sonner and T. Wiseman, Holographic superconductivity in M-theory, Phys. Rev. Lett. 103 (2009) 151601 [arXiv:0907.3796] [INSPIRE].
S.S. Gubser, C.P. Herzog, S.S. Pufu and T. Tesileanu, Superconductors from Superstrings, Phys. Rev. Lett. 103 (2009) 141601 [arXiv:0907.3510] [INSPIRE].
S. Nakamura, H. Ooguri and C.-S. Park, Gravity Dual of Spatially Modulated Phase, Phys. Rev. D 81 (2010) 044018 [arXiv:0911.0679] [INSPIRE].
H. Ooguri and C.-S. Park, Holographic End-Point of Spatially Modulated Phase Transition, Phys. Rev. D 82 (2010) 126001 [arXiv:1007.3737] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic striped phases, JHEP 08 (2011) 140 [arXiv:1106.2004] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic helical superconductors, JHEP 12 (2011) 091 [arXiv:1109.3866] [INSPIRE].
A. Donos, J.P. Gauntlett and C. Pantelidou, Spatially modulated instabilities of magnetic black branes, JHEP 01 (2012) 061 [arXiv:1109.0471] [INSPIRE].
A. Donos, J.P. Gauntlett and C. Pantelidou, Magnetic and Electric AdS Solutions in String-and M-theory, Class. Quant. Grav. 29 (2012) 194006 [arXiv:1112.4195] [INSPIRE].
S.K. Domokos and J.A. Harvey, Baryon number-induced Chern-Simons couplings of vector and axial-vector mesons in holographic QCD, Phys. Rev. Lett. 99 (2007) 141602 [arXiv:0704.1604] [INSPIRE].
H. Ooguri and C.-S. Park, Spatially Modulated Phase in Holographic quark-gluon Plasma, Phys. Rev. Lett. 106 (2011) 061601 [arXiv:1011.4144] [INSPIRE].
C.B. Bayona, K. Peeters and M. Zamaklar, A Non-homogeneous ground state of the low-temperature Sakai-Sugimoto model, JHEP 06 (2011) 092 [arXiv:1104.2291] [INSPIRE].
O. Bergman, N. Jokela, G. Lifschytz and M. Lippert, Striped instability of a holographic Fermi-like liquid, JHEP 10 (2011) 034 [arXiv:1106.3883] [INSPIRE].
A. Donos and J.P. Gauntlett, Helical superconducting black holes, Phys. Rev. Lett. 108 (2012)211601 [arXiv:1203.0533] [INSPIRE].
A. Donos and J.P. Gauntlett, Black holes dual to helical current phases, Phys. Rev. D 86 (2012)064010 [arXiv:1204.1734] [INSPIRE].
N. Iizuka et al., Bianchi Attractors: a Classification of Extremal Black Brane Geometries, JHEP 07 (2012) 193 [arXiv:1201.4861] [INSPIRE].
M. Rozali, D. Smyth, E. Sorkin and J.B. Stang, Holographic Stripes, arXiv:1211.5600 [INSPIRE].
G. Lifschytz and M. Lippert, Holographic Magnetic Phase Transition, Phys. Rev. D 80 (2009)066007 [arXiv:0906.3892] [INSPIRE].
C. Charmousis, B. Gouteraux, B. Kim, E. Kiritsis and R. Meyer, Effective Holographic Theories for low-temperature condensed matter systems, JHEP 11 (2010) 151 [arXiv:1005.4690] [INSPIRE].
N. Ogawa, T. Takayanagi and T. Ugajin, Holographic Fermi Surfaces and Entanglement Entropy, JHEP 01 (2012) 125 [arXiv:1111.1023] [INSPIRE].
L. Huijse, S. Sachdev and B. Swingle, Hidden Fermi surfaces in compressible states of gauge-gravity duality, Phys. Rev. B 85 (2012) 035121 [arXiv:1112.0573] [INSPIRE].
J.P. Gauntlett, J. Sonner and T. Wiseman, Quantum Criticality and Holographic Superconductors in M-theory, JHEP 02 (2010) 060 [arXiv:0912.0512] [INSPIRE].
X. Dong, S. Harrison, S. Kachru, G. Torroba and H. Wang, Aspects of holography for theories with hyperscaling violation, JHEP 06 (2012) 041 [arXiv:1201.1905] [INSPIRE].
H. Singh, Lifshitz/Schródinger Dp-branes and dynamical exponents, JHEP 07 (2012) 082 [arXiv:1202.6533] [INSPIRE].
K. Narayan, On Lifshitz scaling and hyperscaling violation in string theory, Phys. Rev. D 85 (2012)106006 [arXiv:1202.5935] [INSPIRE].
P. Dey and S. Roy, Lifshitz-like space-time from intersecting branes in string/M theory, JHEP 06 (2012) 129 [arXiv:1203.5381] [INSPIRE].
J.P. Gauntlett, S. Kim, O. Varela and D. Waldram, Consistent supersymmetric Kaluza-Klein truncations with massive modes, JHEP 04 (2009) 102 [arXiv:0901.0676] [INSPIRE].
M. Duff, B. Nilsson and C. Pope, The criterion for vacuum stability in Kaluza-Klein supergravity, Phys. Lett. B 139 (1984) 154 [INSPIRE].
A. Imaanpur and M. Naghdi, Dual Instantons in Anti-membranes Theory, Phys. Rev. D 83 (2011)085025 [arXiv:1012.2554] [INSPIRE].
D. Forcella and A. Zaffaroni, Non-supersymmetric CS-matter theories with known AdS duals, Adv. High Energy Phys. 2011 (2011) 393645 [arXiv:1103.0648] [INSPIRE].
F. Denef and S.A. Hartnoll, Landscape of superconducting membranes, Phys. Rev. D 79 (2009)126008 [arXiv:0901.1160] [INSPIRE].
M. Taylor, Non-relativistic holography, arXiv:0812.0530 [INSPIRE].
S.S. Gubser and F.D. Rocha, Peculiar properties of a charged dilatonic black hole in AdS 5, Phys. Rev. D 81 (2010) 046001 [arXiv:0911.2898] [INSPIRE].
K. Goldstein, S. Kachru, S. Prakash and S.P. Trivedi, Holography of Charged Dilaton Black Holes, JHEP 08 (2010) 078 [arXiv:0911.3586] [INSPIRE].
K. Goldstein et al., Holography of Dyonic Dilaton Black Branes, JHEP 10 (2010) 027 [arXiv:1007.2490] [INSPIRE].
F. Denef, S.A. Hartnoll and S. Sachdev, Quantum oscillations and black hole ringing, Phys. Rev. D 80 (2009) 126016 [arXiv:0908.1788] [INSPIRE].
S.A. Hartnoll and P. Kovtun, Hall conductivity from dyonic black holes, Phys. Rev. D 76 (2007)066001 [arXiv:0704.1160] [INSPIRE].
V. Balasubramanian and P. Kraus, A Stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
T. Albash and C.V. Johnson, A Holographic Superconductor in an External Magnetic Field, JHEP 09 (2008) 121 [arXiv:0804.3466] [INSPIRE].
K. Maeda, M. Natsuume and T. Okamura, Vortex lattice for a holographic superconductor, Phys. Rev. D 81 (2010) 026002 [arXiv:0910.4475] [INSPIRE].
S.A. Grigera et al., Disorder-Sensitive Phase Formation Linked to Metamagnetic Quantum Criticality, Science 12 (2004) 1154.
A.J. Millis, A.J. Schofield, G.G. Lonzarich and S.A. Grigera, Metamagnetic Quantum Criticality in Metals, Physical Review Letters 88 (2002) 217204 [cond-mat/0109440].
E. D’Hoker and P. Kraus, Holographic Metamagnetism, Quantum Criticality and Crossover Behavior, JHEP 05 (2010) 083 [arXiv:1003.1302] [INSPIRE].
E. D’Hoker and P. Kraus, Magnetic Brane Solutions in AdS, JHEP 10 (2009) 088 [arXiv:0908.3875] [INSPIRE].
E. D’Hoker and P. Kraus, Charged Magnetic Brane Solutions in AdS 5 and the fate of the third law of thermodynamics, JHEP 03 (2010) 095 [arXiv:0911.4518] [INSPIRE].
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ArXiv ePrint: 1212.0871
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Donos, A., Gauntlett, J.P., Sonner, J. et al. Competing orders in M-theory: superfluids, stripes and metamagnetism. J. High Energ. Phys. 2013, 108 (2013). https://doi.org/10.1007/JHEP03(2013)108
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DOI: https://doi.org/10.1007/JHEP03(2013)108