Abstract
We investigate the holographic dual of a probe scalar in an asymptotically Anti-de-Sitter (AdS) disordered background which is an exact solution of Einstein’s equations in three bulk dimensions. Unlike other approaches to model disorder in holography, we are able to explore quantum wave-like interference effects between an oscillating or random source and the geometry. In the weak-disorder limit, we compute analytically and numerically the one-point correlation function of the dual field theory for different choices of sources and backgrounds. The most interesting feature is the suppression of the one-point function in the presence of an oscillating source and weak random background. We have also computed analytically and numerically the two-point function in the weak disorder limit. We have found that, in general, the perturbative contribution induces an additional power-law decay whose exponent depends on the distribution of disorder. For certain choices of the gravity background, this contribution becomes dominant for large separations which indicates breaking of perturbation theory and the possible existence of a phase transition induced by disorder.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P.W. Anderson, Absence of Diffusion in Certain Random Lattices, Phys. Rev. 109 (1958) 1492 [INSPIRE].
R. Abou-Chacra, D.J. Thouless and P.W. Anderson, A selfconsistent theory of localization, J. Phys. C 6 (1973) 1734.
D. Basko, I. Aleiner and B. Altshuler, Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states, Annals Phys. 321 (2006) 1126.
S. John, Electromagnetic absorption in a disordered medium near a photon mobility edge, Phys. Rev. Lett. 53 (1984) 2169.
P.W. Anderson, The question of classical localization a theory of white paint?, Phil. Mag. B 52 (1985) 505.
Y. Bardoux, M.M. Caldarelli and C. Charmousis, Shaping black holes with free fields, JHEP 05 (2012) 054 [arXiv:1202.4458] [INSPIRE].
T. Andrade and B. Withers, A simple holographic model of momentum relaxation, JHEP 05 (2014) 101 [arXiv:1311.5157] [INSPIRE].
T. Andrade, S.A. Gentle and B. Withers, Drude in D major, JHEP 06 (2016) 134 [arXiv:1512.06263] [INSPIRE].
T. Andrade, A simple model of momentum relaxation in Lifshitz holography, arXiv:1602.00556 [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].
R.A. Davison and B. Goutéraux, Momentum dissipation and effective theories of coherent and incoherent transport, JHEP 01 (2015) 039 [arXiv:1411.1062] [INSPIRE].
A. Amoretti, A. Braggio, N. Maggiore, N. Magnoli and D. Musso, Thermo-electric transport in gauge/gravity models with momentum dissipation, JHEP 09 (2014) 160 [arXiv:1406.4134] [INSPIRE].
R.A. Davison and B. Goutéraux, Dissecting holographic conductivities, JHEP 09 (2015) 090 [arXiv:1505.05092] [INSPIRE].
M. Baggioli and O. Pujolàs, On holographic disorder-driven metal-insulator transitions, JHEP 01 (2017) 040 [arXiv:1601.07897] [INSPIRE].
B. Goutéraux, E. Kiritsis and W.-J. Li, Effective holographic theories of momentum relaxation and violation of conductivity bound, JHEP 04 (2016) 122 [arXiv:1602.01067] [INSPIRE].
A.M. García-García, B. Loureiro and A. Romero-Bermúdez, Transport in a gravity dual with a varying gravitational coupling constant, Phys. Rev. D 94 (2016) 086007 [arXiv:1606.01142] [INSPIRE].
S.A. Hartnoll and C.P. Herzog, Impure AdS/CFT correspondence, Phys. Rev. D 77 (2008) 106009 [arXiv:0801.1693] [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].
A. Lucas and S. Sachdev, Memory matrix theory of magnetotransport in strange metals, Phys. Rev. B 91 (2015) 195122 [arXiv:1502.04704] [INSPIRE].
A. Lucas, Conductivity of a strange metal: from holography to memory functions, JHEP 03 (2015) 071 [arXiv:1501.05656] [INSPIRE].
A. Donos and S.A. Hartnoll, Interaction-driven localization in holography, Nature Phys. 9 (2013) 649 [arXiv:1212.2998] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic Q-lattices, JHEP 04 (2014) 040 [arXiv:1311.3292] [INSPIRE].
A. Donos, B. Goutéraux and E. Kiritsis, Holographic Metals and Insulators with Helical Symmetry, JHEP 09 (2014) 038 [arXiv:1406.6351] [INSPIRE].
D. Vegh, Holography without translational symmetry, arXiv:1301.0537 [INSPIRE].
M. Blake and D. Tong, Universal Resistivity from Holographic Massive Gravity, Phys. Rev. D 88 (2013) 106004 [arXiv:1308.4970] [INSPIRE].
R.A. Davison, Momentum relaxation in holographic massive gravity, Phys. Rev. D 88 (2013) 086003 [arXiv:1306.5792] [INSPIRE].
M. Baggioli and O. Pujolàs, Electron-Phonon Interactions, Metal-Insulator Transitions and Holographic Massive Gravity, Phys. Rev. Lett. 114 (2015) 251602 [arXiv:1411.1003] [INSPIRE].
F. Aprile and T. Ishii, A Simple Holographic Model of a Charged Lattice, JHEP 10 (2014) 151 [arXiv:1406.7193] [INSPIRE].
A. Donos and J.P. Gauntlett, The thermoelectric properties of inhomogeneous holographic lattices, JHEP 01 (2015) 035 [arXiv:1409.6875] [INSPIRE].
S. Kachru, A. Karch and S. Yaida, Holographic Lattices, Dimers and Glasses, Phys. Rev. D 81 (2010) 026007 [arXiv:0909.2639] [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].
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].
P. Chesler, A. Lucas and S. Sachdev, Conformal field theories in a periodic potential: results from holography and field theory, Phys. Rev. D 89 (2014) 026005 [arXiv:1308.0329] [INSPIRE].
M. Fujita, Y. Hikida, S. Ryu and T. Takayanagi, Disordered Systems and the Replica Method in AdS/CFT, JHEP 12 (2008) 065 [arXiv:0810.5394] [INSPIRE].
O. Aharony, Z. Komargodski and S. Yankielowicz, Disorder in Large-N Theories, JHEP 04 (2016) 013 [arXiv:1509.02547] [INSPIRE].
J. Cardy, Logarithmic conformal field theories as limits of ordinary CFTs and some physical applications, J. Phys. A 46 (2013) 494001 [arXiv:1302.4279] [INSPIRE].
S. Ryu, T. Takayanagi and T. Ugajin, Holographic Conductivity in Disordered Systems, JHEP 04 (2011) 115 [arXiv:1103.6068] [INSPIRE].
O. Saremi, Disorder in Gauge/Gravity Duality, Pole Spectrum Statistics and Random Matrix Theory, Class. Quant. Grav. 31 (2014) 095014 [arXiv:1206.1856] [INSPIRE].
H.B. Zeng, Possible Anderson localization in a holographic superconductor, Phys. Rev. D 88 (2013) 126004 [arXiv:1310.5753] [INSPIRE].
M. Taylor and W. Woodhead, Inhomogeneity simplified, Eur. Phys. J. C 74 (2014) 3176 [arXiv:1406.4870] [INSPIRE].
D. Arean, A. Farahi, L.A. Pando Zayas, I.S. Landea and A. Scardicchio, Holographic superconductor with disorder, Phys. Rev. D 89 (2014) 106003 [arXiv:1308.1920] [INSPIRE].
D. Areán, A. Farahi, L.A. Pando Zayas, I. Salazar Landea and A. Scardicchio, Holographic p-wave Superconductor with Disorder, JHEP 07 (2015) 046 [arXiv:1407.7526] [INSPIRE].
D. Arean, L.A. Pando Zayas, I.S. Landea and A. Scardicchio, Holographic disorder driven superconductor-metal transition, Phys. Rev. D 94 (2016) 106003 [arXiv:1507.02280] [INSPIRE].
A. Lucas and S. Sachdev, Conductivity of weakly disordered strange metals: from conformal to hyperscaling-violating regimes, Nucl. Phys. B 892 (2015) 239 [arXiv:1411.3331] [INSPIRE].
M. Araujo, D. Arean and J.M. Lizana, Noisy branes, JHEP 07 (2016) 091 [arXiv:1603.09625] [INSPIRE].
A. Adams and S. Yaida, Disordered holographic systems: Functional renormalization, Phys. Rev. D 92 (2015) 126008 [arXiv:1102.2892] [INSPIRE].
A. Adams and S. Yaida, Disordered holographic systems: Marginal relevance of imperfection, Phys. Rev. D 90 (2014) 046007 [arXiv:1201.6366] [INSPIRE].
S.A. Hartnoll and J.E. Santos, Disordered horizons: Holography of randomly disordered fixed points, Phys. Rev. Lett. 112 (2014) 231601 [arXiv:1402.0872] [INSPIRE].
S.A. Hartnoll, D.M. Ramirez and J.E. Santos, Emergent scale invariance of disordered horizons, JHEP 09 (2015) 160 [arXiv:1504.03324] [INSPIRE].
S.A. Hartnoll, D.M. Ramirez and J.E. Santos, Thermal conductivity at a disordered quantum critical point, JHEP 04 (2016) 022 [arXiv:1508.04435] [INSPIRE].
S.A. Hartnoll, D.M. Ramirez and J.E. Santos, Entropy production, viscosity bounds and bumpy black holes, JHEP 03 (2016) 170 [arXiv:1601.02757] [INSPIRE].
D.K. O’Keeffe and A.W. Peet, Perturbatively charged holographic disorder, Phys. Rev. D 92 (2015) 046004 [arXiv:1504.03288] [INSPIRE].
A.M. García-García and B. Loureiro, Marginal and Irrelevant Disorder in Einstein-Maxwell backgrounds, Phys. Rev. D 93 (2016) 065025 [arXiv:1512.00194] [INSPIRE].
A. Donos and J.P. Gauntlett, On the thermodynamics of periodic AdS black branes, JHEP 10 (2013) 038 [arXiv:1306.4937] [INSPIRE].
A. Donos and J.P. Gauntlett, Thermoelectric DC conductivities from black hole horizons, JHEP 11 (2014) 081 [arXiv:1406.4742] [INSPIRE].
A. Donos and J.P. Gauntlett, Navier-Stokes Equations on Black Hole Horizons and DC Thermoelectric Conductivity, Phys. Rev. D 92 (2015) 121901 [arXiv:1506.01360] [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. Donos, J.P. Gauntlett and V. Ziogas, Diffusion in inhomogeneous media, Phys. Rev. D 96 (2017) 125003 [arXiv:1708.05412] [INSPIRE].
S. Grozdanov, A. Lucas, S. Sachdev and K. Schalm, Absence of disorder-driven metal-insulator transitions in simple holographic models, Phys. Rev. Lett. 115 (2015) 221601 [arXiv:1507.00003] [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].
T.N. Ikeda, A. Lucas and Y. Nakai, Conductivity bounds in probe brane models, JHEP 04 (2016) 007 [arXiv:1601.07882] [INSPIRE].
A. Lucas, Hydrodynamic transport in strongly coupled disordered quantum field theories, New J. Phys. 17 (2015) 113007 [arXiv:1506.02662] [INSPIRE].
B.L. Altshuler, D. Khmel’nitzkii, A.I. Larkin and P.A. Lee, Magnetoresistance and hall effect in a disordered two-dimensional electron gas, Phys. Rev. B B 22 (1980) 5142.
C. Fefferman and C. R. Graham, The ambient metric, arXiv:0710.0919.
C. Fefferman and C.R. Graham, Conformal Invariants, in Élie Cartan et les Mathématiques d’aujourd’hui, Société mathématique de France, Paris France (1985), pg. 95.
K. Skenderis and S.N. Solodukhin, Quantum effective action from the AdS/CFT correspondence, Phys. Lett. B 472 (2000) 316 [hep-th/9910023].
P. Breitenlohner and D.Z. Freedman, Positive Energy in anti-de Sitter Backgrounds and Gauged Extended Supergravity, Phys. Lett. 115B (1982) 197 [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Stability in Gauged Extended Supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].
R.A. Janik, J. Jankowski and P. Witkowski, Conformal defects in supergravity-backreacted Dirac delta sources, JHEP 07 (2015) 050 [arXiv:1503.08459] [INSPIRE].
C. Li and J. Lucietti, Three-dimensional black holes and descendants, Phys. Lett. B 738 (2014) 48 [arXiv:1312.2626] [INSPIRE].
K. Skenderis, Lecture notes on holographic renormalization, Class. Quant. Grav. 19 (2002) 5849 [hep-th/0209067] [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: 1711.10953
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Andrade, T., García-García, A.M. & Loureiro, B. Coherence effects in disordered geometries with a field-theory dual. J. High Energ. Phys. 2018, 187 (2018). https://doi.org/10.1007/JHEP03(2018)187
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2018)187