Abstract
In the context of applications of the AdS/CFT correspondence to condensed matter physics, we compute conductivities for field theory duals of dyonic planar black holes in 3+1-dimensional Einstein-Maxwell-dilaton theories at zero temperature. We combine the near-horizon data obtained via Sen’s entropy function formalism with known expressions for conductivities. In this way we express the conductivities in terms of the extremal black hole charges. We apply our approach to three different examples for dilaton theories for which the background geometry is not known explicitly. For a constant scalar potential, the thermoelectric conductivity explicitly scales as α xy ∼ N 3/2, as expected. For the same model, our approach yields a finite result for the heat conductivity κ/T ∝ N 3/2 even for T → 0.
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References
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].
S.A. Hartnoll and P. Kovtun, Hall conductivity from dyonic black holes, Phys. Rev. D 76 (2007) 066001 [arXiv:0704.1160] [INSPIRE].
A. Donos, J.P. Gauntlett, T. Griffin and L. Melgar, DC Conductivity of Magnetised Holographic Matter, JHEP 01 (2016) 113 [arXiv:1511.00713] [INSPIRE].
A. Amoretti, M. Baggioli, N. Magnoli and D. Musso, Chasing the cuprates with dilatonic dyons, JHEP 06 (2016) 113 [arXiv:1603.03029] [INSPIRE].
J. Erdmenger, B. Herwerth, S. Klug, R. Meyer and K. Schalm, S-Wave Superconductivity in Anisotropic Holographic Insulators, JHEP 05 (2015) 094 [arXiv:1501.07615] [INSPIRE].
K.-Y. Kim and C. Niu, Homes’ law in Holographic Superconductor with Q-lattices, JHEP 10 (2016) 144 [arXiv:1608.04653] [INSPIRE].
M. Blake and D. Tong, Universal Resistivity from Holographic Massive Gravity, Phys. Rev. D 88 (2013) 106004 [arXiv:1308.4970] [INSPIRE].
A. Donos and J.P. Gauntlett, Novel metals and insulators from holography, JHEP 06 (2014) 007 [arXiv:1401.5077] [INSPIRE].
A. Donos and J.P. Gauntlett, Thermoelectric DC conductivities from black hole horizons, JHEP 11 (2014) 081 [arXiv:1406.4742] [INSPIRE].
M. Blake, A. Donos and N. Lohitsiri, Magnetothermoelectric Response from Holography, JHEP 08 (2015) 124 [arXiv:1502.03789] [INSPIRE].
J. Lindgren, I. Papadimitriou, A. Taliotis and J. Vanhoof, Holographic Hall conductivities from dyonic backgrounds, JHEP 07 (2015) 094 [arXiv:1505.04131] [INSPIRE].
A. Sen, Black hole entropy function and the attractor mechanism in higher derivative gravity, JHEP 09 (2005) 038 [hep-th/0506177] [INSPIRE].
D. Astefanesei, N. Banerjee and S. Dutta, Near horizon data and physical charges of extremal AdS black holes, Nucl. Phys. B 853 (2011) 63 [arXiv:1104.4121] [INSPIRE].
N. Kundu, P. Narayan, N. Sircar and S.P. Trivedi, Entangled Dilaton Dyons, JHEP 03 (2013) 155 [arXiv:1208.2008] [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, N. Iizuka, S. Kachru, S. Prakash, S.P. Trivedi and A. Westphal, Holography of Dyonic Dilaton Black Branes, JHEP 10 (2010) 027 [arXiv:1007.2490] [INSPIRE].
A.D. Shapere, S. Trivedi and F. Wilczek, Dual dilaton dyons, Mod. Phys. Lett. A 6 (1991) 2677 [INSPIRE].
R. Kallosh, A.D. Linde, T. Ortín, A.W. Peet and A. Van Proeyen, Supersymmetry as a cosmic censor, Phys. Rev. D 46 (1992) 5278 [hep-th/9205027] [INSPIRE].
M. Cadoni and P. Pani, Holography of charged dilatonic black branes at finite temperature, JHEP 04 (2011) 049 [arXiv:1102.3820] [INSPIRE].
A. Sen, Black Hole Entropy Function, Attractors and Precision Counting of Microstates, Gen. Rel. Grav. 40 (2008) 2249 [arXiv:0708.1270] [INSPIRE].
S. Ferrara, R. Kallosh and A. Strominger, N = 2 extremal black holes, Phys. Rev. D 52 (1995) R5412 [hep-th/9508072] [INSPIRE].
S. Ferrara and R. Kallosh, Supersymmetry and attractors, Phys. Rev. D 54 (1996) 1514 [hep-th/9602136] [INSPIRE].
H.K. Kunduri, J. Lucietti and H.S. Reall, Near-horizon symmetries of extremal black holes, Class. Quant. Grav. 24 (2007) 4169 [arXiv:0705.4214] [INSPIRE].
A. Sen, Entropy function for heterotic black holes, JHEP 03 (2006) 008 [hep-th/0508042] [INSPIRE].
B. Sahoo and A. Sen, BTZ black hole with Chern-Simons and higher derivative terms, JHEP 07 (2006) 008 [hep-th/0601228] [INSPIRE].
B. Sahoo and A. Sen, Higher derivative corrections to non-supersymmetric extremal black holes in N = 2 supergravity, JHEP 09 (2006) 029 [hep-th/0603149] [INSPIRE].
M. Alishahiha and H. Ebrahim, Non-supersymmetric attractors and entropy function, JHEP 03 (2006) 003 [hep-th/0601016] [INSPIRE].
B. Chandrasekhar, S. Parvizi, A. Tavanfar and H. Yavartanoo, Non-supersymmetric attractors in R 2 gravities, JHEP 08 (2006) 004 [hep-th/0602022] [INSPIRE].
D. Astefanesei, K. Goldstein, R.P. Jena, A. Sen and S.P. Trivedi, Rotating attractors, JHEP 10 (2006) 058 [hep-th/0606244] [INSPIRE].
R. Kallosh, N. Sivanandam and M. Soroush, The Non-BPS black hole attractor equation, JHEP 03 (2006) 060 [hep-th/0602005] [INSPIRE].
B.R. Majhi, Entropy function from the gravitational surface action for an extremal near horizon black hole, Eur. Phys. J. C 75 (2015) 521 [arXiv:1503.08973] [INSPIRE].
B. Goutéraux, Charge transport in holography with momentum dissipation, JHEP 04 (2014) 181 [arXiv:1401.5436] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic Q-lattices, JHEP 04 (2014) 040 [arXiv:1311.3292] [INSPIRE].
C. Charmousis, B. Gouteraux and J. Soda, Einstein-Maxwell-Dilaton theories with a Liouville potential, Phys. Rev. D 80 (2009) 024028 [arXiv:0905.3337] [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].
S. Moroz, Below the Breitenlohner-Freedman bound in the nonrelativistic AdS/CFT correspondence, Phys. Rev. D 81 (2010) 066002 [arXiv:0911.4060] [INSPIRE].
M. Cadoni, G. D’Appollonio and P. Pani, Phase transitions between Reissner-Nordstrom and dilatonic black holes in 4D AdS spacetime, JHEP 03 (2010) 100 [arXiv:0912.3520] [INSPIRE].
S. Grozdanov, A. Lucas and K. Schalm, Incoherent thermal transport from dirty black holes, Phys. Rev. D 93 (2016) 061901 [arXiv:1511.05970] [INSPIRE].
G.W. Gibbons and K.-i. Maeda, Black Holes and Membranes in Higher Dimensional Theories with Dilaton Fields, Nucl. Phys. B 298 (1988) 741 [INSPIRE].
D. Garfinkle, G.T. Horowitz and A. Strominger, Charged black holes in string theory, Phys. Rev. D 43 (1991) 3140 [Erratum ibid. D 45 (1992) 3888] [INSPIRE].
P. Goulart, Dyonic black holes and dilaton charge in string theory, arXiv:1611.03093 [INSPIRE].
P. Goulart, Massless black holes and charged wormholes in string theory, arXiv:1611.03164 [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 and J.P. Gauntlett, Minimally packed phases in holography, JHEP 03 (2016) 148 [arXiv:1512.06861] [INSPIRE].
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Erdmenger, J., Fernández, D., Goulart, P. et al. Conductivities from attractors. J. High Energ. Phys. 2017, 147 (2017). https://doi.org/10.1007/JHEP03(2017)147
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DOI: https://doi.org/10.1007/JHEP03(2017)147