Abstract
We present a mechanism of momentum relaxation in higher derivative gravity by adding linear scalar fields to the Gauss-Bonnet theory. We analytically computed all of the DC thermoelectric conductivities in this theory by adopting the method given by Donos and Gauntlett in [arXiv:1406.4742]. The results show that the DC electric conductivity is not a monotonic function of the effective impurity parameter β: in the small β limit, the DC conductivity is dominated by the coherent phase, while for larger β, pair creation contribution to the conductivity becomes dominant, signaling an incoherent phase. In addition, the DC heat conductivity is found independent of the Gauss-Bonnet coupling constant.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].
J. McGreevy, Holographic duality with a view toward many-body physics, Adv. High Energy Phys. 2010 (2010) 723105 [arXiv:0909.0518] [INSPIRE].
C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].
G.T. Horowitz, J.E. Santos and D. Tong, Optical conductivity with holographic lattices, JHEP 07 (2012) 168 [arXiv:1204.0519] [INSPIRE].
G.T. Horowitz, J.E. Santos and D. Tong, Further evidence for lattice-induced scaling, JHEP 11 (2012) 102 [arXiv:1209.1098] [INSPIRE].
G.T. Horowitz and J.E. Santos, General relativity and the cuprates, JHEP 06 (2013) 087 [arXiv:1302.6586] [INSPIRE].
A. Donos and S.A. Hartnoll, Interaction-driven localization in holography, Nature Phys. 9 (2013) 649 [arXiv:1212.2998] [INSPIRE].
J. Erdmenger, X.-H. Ge and D.-W. Pang, Striped phases in the holographic insulator/superconductor transition, JHEP 11 (2013) 027 [arXiv:1307.4609] [INSPIRE].
Y. Ling, C. Niu, J.-P. Wu and Z.-Y. Xian, Holographic lattice in Einstein-Maxwell-Dilaton gravity, JHEP 11 (2013) 006 [arXiv:1309.4580] [INSPIRE].
Y. Ling, C. Niu, J. Wu, Z. Xian and H.-b. Zhang, Metal-insulator Transition by Holographic Charge Density Waves, Phys. Rev. Lett. 113 (2014) 091602 [arXiv:1404.0777] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic Q-lattices, JHEP 04 (2014) 040 [arXiv:1311.3292] [INSPIRE].
Y. Ling, P. Liu, C. Niu, J.-P. Wu and Z.-Y. Xian, Holographic superconductor on Q-lattice, JHEP 02 (2015) 059 [arXiv:1410.6761] [INSPIRE].
D. Vegh, Holography without translational symmetry, arXiv:1301.0537 [INSPIRE].
B. Goutéraux, Charge transport in holography with momentum dissipation, JHEP 04 (2014) 181 [arXiv:1401.5436] [INSPIRE].
R.A. Davison, Momentum relaxation in holographic massive gravity, Phys. Rev. D 88 (2013) 086003 [arXiv:1306.5792] [INSPIRE].
M. Blake and D. Tong, Universal Resistivity from Holographic Massive Gravity, Phys. Rev. D 88 (2013) 106004 [arXiv:1308.4970] [INSPIRE].
M. Blake, D. Tong and D. Vegh, Holographic Lattices Give the Graviton an Effective Mass, Phys. Rev. Lett. 112 (2014) 071602 [arXiv:1310.3832] [INSPIRE].
H.B. Zeng and J.-P. Wu, Holographic superconductors from the massive gravity, Phys. Rev. D 90 (2014) 046001 [arXiv:1404.5321] [INSPIRE].
R.A. Davison, K. Schalm and J. Zaanen, Holographic duality and the resistivity of strange metals, Phys. Rev. B 89 (2014) 245116 [arXiv:1311.2451] [INSPIRE].
M. Blake and A. Donos, Quantum Critical Transport and the Hall Angle, Phys. Rev. Lett. 114 (2015) 021601 [arXiv:1406.1659] [INSPIRE].
T. Andrade and B. Withers, A simple holographic model of momentum relaxation, JHEP 05 (2014) 101 [arXiv:1311.5157] [INSPIRE].
K.-Y. Kim, K.K. Kim, Y. Seo and S.-J. Sin, Coherent/incoherent metal transition in a holographic model, JHEP 12 (2014) 170 [arXiv:1409.8346] [INSPIRE].
A. Donos, B. Goutéraux and E. Kiritsis, Holographic Metals and Insulators with Helical Symmetry, JHEP 09 (2014) 038 [arXiv:1406.6351] [INSPIRE].
R.A. Davison and B. Goutéraux, Momentum dissipation and effective theories of coherent and incoherent transport, JHEP 01 (2015) 039 [arXiv:1411.1062] [INSPIRE].
X.-H. Ge, Y. Ling, C. Niu and S.-J. Sin, Holographic transports and stability in anisotropic linear axion model, arXiv:1412.8346 [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 and J.P. Gauntlett, Holographic striped phases, JHEP 08 (2011) 140 [arXiv:1106.2004] [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].
A. Amoretti, A. Braggio, N. Maggiore, N. Magnoli and D. Musso, Analytic DC thermo-electric conductivities in holography with massive gravitons, Phys. Rev. D 91 (2015) 025002 [arXiv:1407.0306].
A. Donos and J.P. Gauntlett, The thermoelectric properties of inhomogeneous holographic lattices, JHEP 01 (2015) 035 [arXiv:1409.6875] [INSPIRE].
R.-G. Cai, Gauss-Bonnet black holes in AdS spaces, Phys. Rev. D 65 (2002) 084014 [hep-th/0109133] [INSPIRE].
M. Cvetič, S. Nojiri and S.D. Odintsov, Black hole thermodynamics and negative entropy in de Sitter and anti-de Sitter Einstein-Gauss-Bonnet gravity, Nucl. Phys. B 628 (2002) 295 [hep-th/0112045] [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].
L. Barclay, R. Gregory, S. Kanno and P. Sutcliffe, Gauss-Bonnet holographic superconductors, JHEP 12 (2010) 029 [arXiv:1009.1991] [INSPIRE].
J. Jing, L. Wang, Q. Pan and S. Chen, Holographic Superconductors in Gauss-Bonnet gravity with Born-Infeld electrodynamics, Phys. Rev. D 83 (2011) 066010 [arXiv:1012.0644] [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].
D. Mateos and D. Trancanelli, Thermodynamics and instabilities of a strongly coupled anisotropic plasma, JHEP 07 (2011) 054 [arXiv:1106.1637] [INSPIRE].
L. Cheng, X.-H. Ge and S.-J. Sin, Anisotropic plasma with a chemical potential and scheme-independent instabilities, Phys. Lett. B 734 (2014) 116 [arXiv:1404.1994] [INSPIRE].
L. Cheng, X.-H. Ge and S.-J. Sin, Anisotropic plasma at finite U(1) chemical potential, JHEP 07 (2014) 083 [arXiv:1404.5027] [INSPIRE].
V. Jahnke, A.S. Misobuchi and D. Trancanelli, Holographic renormalization and anisotropic black branes in higher curvature gravity, JHEP 01 (2015) 122 [arXiv:1411.5964] [INSPIRE].
L.Q. Fang, X.-H. Ge, J.-P. Wu and H.-Q. Leng, Anisotropic Fermi surface from holography, arXiv:1409.6062 [INSPIRE].
S. Carroll, Spacetime and Geometry, Addision-Wesley, Reading U.S.A. (2004).
X.-H. Ge, Y. Ling, Y. Tian and X.-N. Wu, Holographic RG flows and transport coefficients in Einstein-Gauss-Bonnet-Maxwell theory, JHEP 01 (2012) 117 [arXiv:1112.0627] [INSPIRE].
D. Tong, Lectures on holographic conductivity, talk presented at Cracow school of theoretical Physics, Cracow Poland (2013), http://www.damtp.cam.ac.uk/user/tong/talks/zakopane.pdf.
M. Brigante, H. Liu, R.C. Myers, S. Shenker and S. Yaida, Viscosity Bound Violation in Higher Derivative Gravity, Phys. Rev. D 77 (2008) 126006 [arXiv:0712.0805] [INSPIRE].
X.-H. Ge and S.-J. Sin, Shear viscosity, instability and the upper bound of the Gauss-Bonnet coupling constant, JHEP 05 (2009) 051 [arXiv:0903.2527] [INSPIRE].
R.-G. Cai, Z.-Y. Nie and Y.-W. Sun, Shear Viscosity from Effective Couplings of Gravitons, Phys. Rev. D 78 (2008) 126007 [arXiv:0811.1665] [INSPIRE].
X.-H. Ge, S.-J. Sin, S.-F. Wu and G.-H. Yang, Shear viscosity and instability from third order Lovelock gravity, Phys. Rev. D 80 (2009) 104019 [arXiv:0905.2675] [INSPIRE].
R.C. Myers, M.F. Paulos and A. Sinha, Holographic hydrodynamics with a chemical potential, JHEP 06 (2009) 006 [arXiv:0903.2834] [INSPIRE].
X.-H. Ge, Y. Matsuo, F.-W. Shu, S.-J. Sin and T. Tsukioka, Viscosity bound, causality violation and instability with stringy correction and charge, JHEP 10 (2008) 009 [arXiv:0808.2354] [INSPIRE].
A. Bhattacharyya and D. Roychowdhury, Viscosity bound for anisotropic superfluids in higher derivative gravity, JHEP 03 (2015) 063 [arXiv:1410.3222] [INSPIRE].
L.K. Joshi and P. Ramadevi, Backreaction effects due to matter coupled higher derivative gravity, arXiv:1409.8019 [INSPIRE].
V. Balasubramanian and P. Kraus, A stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
Y. Brihaye and E. Radu, Black objects in the Einstein-Gauss-Bonnet theory with negative cosmological constant and the boundary counterterm method, JHEP 09 (2008) 006 [arXiv:0806.1396] [INSPIRE].
J.T. Liu and W.A. Sabra, Hamilton-Jacobi Counterterms for Einstein-Gauss-Bonnet Gravity, Class. Quant. Grav. 27 (2010) 175014 [arXiv:0807.1256] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1411.5452
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Cheng, L., Ge, XH. & Sun, ZY. Thermoelectric DC conductivities with momentum dissipation from higher derivative gravity. J. High Energ. Phys. 2015, 135 (2015). https://doi.org/10.1007/JHEP04(2015)135
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2015)135