Abstract
A model consisting of (d+1)-dimensional gravity coupled to spacetime filling charged branes is used to study the effects of backreaction. The charged black holes arising from this simple model reflect the non-linearity of the gauge field and are thermodynamically stable. By analysing fluctuations of the system we corroborate that at low values of the temperature (or large chemical potential) backreaction effects from the branes are dominant. We also provide a generalisation of the Iqbal and Liu strategy to calculate the DC conductivity, in which a mass term for the gauge field fluctuation is included. This mass term gives the value of the residue of the pole at zero frequency in the imaginary part of the AC conductivity, as well as the running of the DC conductivity with the bulk radius.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].
J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal and U.A. Wiedemann, Gauge/String Duality, Hot QCD and Heavy Ion Collisions, arXiv:1101.0618 [INSPIRE].
F. Benini, Holography and condensed matter, Fortsch. Phys. 60 (2012) 810 [arXiv:1202.6008] [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].
F. Denef and S.A. Hartnoll, Landscape of superconducting membranes, Phys. Rev. D 79 (2009) 126008 [arXiv:0901.1160] [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].
J.P. Gauntlett, J. Sonner and T. Wiseman, Holographic superconductivity in M-theory, Phys. Rev. Lett. 103 (2009) 151601 [arXiv:0907.3796] [INSPIRE].
S. Kachru, X. Liu and M. Mulligan, Gravity duals of Lifshitz-like fixed points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [INSPIRE].
D.T. Son, Toward an AdS/cold atoms correspondence: a geometric realization of the Schrödinger symmetry, Phys. Rev. D 78 (2008) 046003 [arXiv:0804.3972] [INSPIRE].
C.P. Herzog, M. Rangamani and S.F. Ross, Heating up Galilean holography, JHEP 11 (2008) 080 [arXiv:0807.1099] [INSPIRE].
J. Maldacena, D. Martelli and Y. Tachikawa, Comments on string theory backgrounds with non-relativistic conformal symmetry, JHEP 10 (2008) 072 [arXiv:0807.1100] [INSPIRE].
A. Adams, K. Balasubramanian and J. McGreevy, Hot Spacetimes for Cold Atoms, JHEP 11 (2008) 059 [arXiv:0807.1111] [INSPIRE].
M. Taylor, Non-relativistic holography, arXiv:0812.0530 [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].
U. Gürsoy, E. Kiritsis, L. Mazzanti, G. Michalogiorgakis and F. Nitti, Improved Holographic QCD, Lect. Notes Phys. 828 (2011) 79 [arXiv:1006.5461] [INSPIRE].
M. Jarvinen and E. Kiritsis, Holographic Models for QCD in the Veneziano Limit, JHEP 03 (2012) 002 [arXiv:1112.1261] [INSPIRE].
T. Alho, M. Järvinen, K. Kajantie, E. Kiritsis and K. Tuominen, On finite-temperature holographic QCD in the Veneziano limit, JHEP 01 (2013) 093 [arXiv:1210.4516] [INSPIRE].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].
S.A. Hartnoll, J. Polchinski, E. Silverstein and D. Tong, Towards strange metallic holography, JHEP 04 (2010) 120 [arXiv:0912.1061] [INSPIRE].
F. Bigazzi, A.L. Cotrone and J. Tarrio, Charged D3-D7 plasmas: novel solutions, extremality and stability issues, JHEP 07 (2013) 074 [arXiv:1304.4802] [INSPIRE].
H.-C. Chang and A. Karch, Entanglement Entropy for Probe Branes, JHEP 01 (2014) 180 [arXiv:1307.5325] [INSPIRE].
K. Jensen and A. O’Bannon, Holography, Entanglement Entropy and Conformal Field Theories with Boundaries or Defects, Phys. Rev. D 88 (2013) 106006 [arXiv:1309.4523] [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].
B. Gouteraux and E. Kiritsis, Generalized Holographic Quantum Criticality at Finite Density, JHEP 12 (2011) 036 [arXiv:1107.2116] [INSPIRE].
S.S. Pal, Fermi-like Liquid From Einstein-DBI-Dilaton System, JHEP 04 (2013) 007 [arXiv:1209.3559] [INSPIRE].
V. Balasubramanian and P. Kraus, A stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
S. Harrison, S. Kachru and H. Wang, Resolving Lifshitz Horizons, JHEP 02 (2014) 085 [arXiv:1202.6635] [INSPIRE].
J. Bhattacharya, S. Cremonini and A. Sinkovics, On the IR completion of geometries with hyperscaling violation, JHEP 02 (2013) 147 [arXiv:1208.1752] [INSPIRE].
C. Hoyos-Badajoz, A. O’Bannon and J.M.S. Wu, Zero Sound in Strange Metallic Holography, JHEP 09 (2010) 086 [arXiv:1007.0590] [INSPIRE].
J. Mas and J. Tarrio, Hydrodynamics from the Dp-brane, JHEP 05 (2007) 036 [hep-th/0703093] [INSPIRE].
G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics, JHEP 09 (2002) 043 [hep-th/0205052] [INSPIRE].
N. Iqbal and H. Liu, Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm, Phys. Rev. D 79 (2009) 025023 [arXiv:0809.3808] [INSPIRE].
A. Karch and A. O’Bannon, Metallic AdS/CFT, JHEP 09 (2007) 024 [arXiv:0705.3870] [INSPIRE].
S.A. Hartnoll, P.K. Kovtun, M. Muller and S. Sachdev, Theory of the Nernst effect near quantum phase transitions in condensed matter and in dyonic black holes, Phys. Rev. B 76 (2007) 144502 [arXiv:0706.3215] [INSPIRE].
S.A. Hartnoll and C.P. Herzog, Ohm’s Law at strong coupling: S duality and the cyclotron resonance, Phys. Rev. D 76 (2007) 106012 [arXiv:0706.3228] [INSPIRE].
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].
M. Kaminski, K. Landsteiner, J. Mas, J.P. Shock and J. Tarrio, Holographic Operator Mixing and Quasinormal Modes on the Brane, JHEP 02 (2010) 021 [arXiv:0911.3610] [INSPIRE].
P. Kovtun, D.T. Son and A.O. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev. Lett. 94 (2005) 111601 [hep-th/0405231] [INSPIRE].
P. Kovtun, Lectures on hydrodynamic fluctuations in relativistic theories, J. Phys. A 45 (2012) 473001 [arXiv:1205.5040] [INSPIRE].
J. Mas, J.P. Shock and J. Tarrio, A note on conductivity and charge diffusion in holographic flavour systems, JHEP 01 (2009) 025 [arXiv:0811.1750] [INSPIRE].
A. Karch, D.T. Son and A.O. Starinets, Zero Sound from Holography, arXiv:0806.3796 [INSPIRE].
R.A. Davison and A.O. Starinets, Holographic zero sound at finite temperature, Phys. Rev. D 85 (2012) 026004 [arXiv:1109.6343] [INSPIRE].
M. Edalati, J.I. Jottar and R.G. Leigh, Holography and the sound of criticality, JHEP 10 (2010) 058 [arXiv:1005.4075] [INSPIRE].
R.A. Davison and N.K. Kaplis, Bosonic excitations of the AdS 4 Reissner-Nordstrom black hole, JHEP 12 (2011) 037 [arXiv:1111.0660] [INSPIRE].
R.A. Davison and A. Parnachev, Hydrodynamics of cold holographic matter, JHEP 06 (2013) 100 [arXiv:1303.6334] [INSPIRE].
M. Edalati, J.I. Jottar and R.G. Leigh, Transport Coefficients at Zero Temperature from Extremal Black Holes, JHEP 01 (2010) 018 [arXiv:0910.0645] [INSPIRE].
M. Edalati, J.I. Jottar and R.G. Leigh, Shear Modes, Criticality and Extremal Black Holes, JHEP 04 (2010) 075 [arXiv:1001.0779] [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: 1312.2902
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
Tarrío, J. Transport properties of spacetime-filling branes. J. High Energ. Phys. 2014, 42 (2014). https://doi.org/10.1007/JHEP04(2014)042
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2014)042