Abstract
We construct cohomogeneity-three, finite temperature stationary black brane solutions dual to a field theory exhibiting checkerboard order. The checkerboards form a backreacted part of the bulk solution, and are obtained numerically from the coupled Einstein-Maxwell-scalar PDE system. They arise spontaneously and without the inclusion of an explicit lattice. The phase exhibits both charge and global U(1)-current modulation, which are periodic in two spatial directions. The current circulates within each checkerboard plaquette. We explore the competition with striped phases, finding first-order checkerboard to stripe phase transitions.
We also detail spatially modulated instabilities of asymptotically AdS black brane backgrounds with neutral scalar profiles, including those with an hyperscaling violating IR geometry at zero temperature.
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References
M. Vojta, Lattice symmetry breaking in cuprate superconductors: stripes, nematics, and superconductivity, Adv. Phys. 58 (2009) 699 [arXiv:0901.3145].
A. Donos and J.P. Gauntlett, Holographic striped phases, JHEP 08 (2011) 140 [arXiv:1106.2004] [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].
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].
A. Donos, J.P. Gauntlett and C. Pantelidou, Spatially modulated instabilities of magnetic black branes, JHEP 01 (2012) 061 [arXiv:1109.0471] [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.A.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, Holographic charge density waves, Phys. Rev. D 87 (2013) 126008 [arXiv:1303.4398] [INSPIRE].
A. Donos, Striped phases from holography, JHEP 05 (2013) 059 [arXiv:1303.7211] [INSPIRE].
B. Withers, Black branes dual to striped phases, Class. Quant. Grav. 30 (2013) 155025 [arXiv:1304.0129] [INSPIRE].
M. Rozali, D. Smyth, E. Sorkin and J.B. Stang, Holographic stripes, Phys. Rev. Lett. 110 (2013) 201603 [arXiv:1211.5600] [INSPIRE].
B. Withers, The moduli space of striped black branes, arXiv:1304.2011 [INSPIRE].
M. Rozali, D. Smyth, E. Sorkin and J.B. Stang, Striped order in AdS/CFT correspondence, Phys. Rev. D 87 (2013) 126007 [arXiv:1304.3130] [INSPIRE].
A. Donos and J.P. Gauntlett, On the thermodynamics of periodic AdS black branes, JHEP 10 (2013) 038 [arXiv:1306.4937] [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].
J.P. Gauntlett, J. Sonner and T. Wiseman, Quantum criticality and holographic superconductors in M-theory, JHEP 02 (2010) 060 [arXiv:0912.0512] [INSPIRE].
A. Donos, J.P. Gauntlett, J. Sonner and B. Withers, Competing orders in M-theory: superfluids, stripes and metamagnetism, JHEP 03 (2013) 108 [arXiv:1212.0871] [INSPIRE].
M. Headrick, S. Kitchen and T. Wiseman, A new approach to static numerical relativity and its application to Kaluza-Klein black holes, Class. Quant. Grav. 27 (2010) 035002 [arXiv:0905.1822] [INSPIRE].
A. Adam, S. Kitchen and T. Wiseman, A numerical approach to finding general stationary vacuum black holes, Class. Quant. Grav. 29 (2012) 165002 [arXiv:1105.6347] [INSPIRE].
T. Wiseman, Numerical construction of static and stationary black holes, arXiv:1107.5513 [INSPIRE].
F. Denef and S.A. Hartnoll, Landscape of superconducting membranes, Phys. Rev. D 79 (2009) 126008 [arXiv:0901.1160] [INSPIRE].
C. Charmousis, B. Gouteraux, B.S. Kim, E. Kiritsis and R. Meyer, Effective holographic theories for low-temperature condensed matter systems, JHEP 11 (2010) 151 [arXiv:1005.4690] [INSPIRE].
B. Gouteraux and E. Kiritsis, Generalized holographic quantum criticality at finite density, JHEP 12 (2011) 036 [arXiv:1107.2116] [INSPIRE].
Y.-Y. Bu, J. Erdmenger, J.P. Shock and M. Strydom, Magnetic field induced lattice ground states from holography, JHEP 03 (2013) 165 [arXiv:1210.6669] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic Q-lattices, JHEP 04 (2014) 040 [arXiv:1311.3292] [INSPIRE].
T. Andrade and B. Withers, A simple holographic model of momentum relaxation, JHEP 05 (2014) 101 [arXiv:1311.5157] [INSPIRE].
D. Vegh, Holography without translational symmetry, arXiv:1301.0537 [INSPIRE].
R.A. Davison, Momentum relaxation in holographic massive gravity, Phys. Rev. D 88 (2013) 086003 [arXiv:1306.5792] [INSPIRE].
M. Blake, D. Tong and D. Vegh, Holographic lattices give the graviton a mass, Phys. Rev. Lett. 112 (2014) 071602 [arXiv:1310.3832] [INSPIRE].
Y. Bardoux, M.M. Caldarelli and C. Charmousis, Shaping black holes with free fields, JHEP 05 (2012) 054 [arXiv:1202.4458] [INSPIRE].
M. Taylor and W. Woodhead, Inhomogeneity simplified, arXiv:1406.4870 [INSPIRE].
B. Goutéraux, Charge transport in holography with momentum dissipation, JHEP 04 (2014) 181 [arXiv:1401.5436] [INSPIRE].
N. Iizuka et al., Bianchi attractors: a classification of extremal black brane geometries, JHEP 07 (2012) 193 [arXiv:1201.4861] [INSPIRE].
A. Donos and J.P. Gauntlett, Helical superconducting black holes, Phys. Rev. Lett. 108 (2012) 211601 [arXiv:1203.0533] [INSPIRE].
V. Balasubramanian and P. Kraus, A stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
M. Bianchi, D.Z. Freedman and K. Skenderis, Holographic renormalization, Nucl. Phys. B 631 (2002) 159 [hep-th/0112119] [INSPIRE].
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Withers, B. Holographic checkerboards. J. High Energ. Phys. 2014, 102 (2014). https://doi.org/10.1007/JHEP09(2014)102
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DOI: https://doi.org/10.1007/JHEP09(2014)102