Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm
We show that at the level of linear response the low-frequency limit of a strongly coupled field theory at finite temperature is determined by the horizon geometry of its gravity dual, i.e., by the “membrane paradigm” fluid of classical black hole mechanics. Thus, generic boundary theory transport c...
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| Format: | Article |
| Language: | en_US |
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American Physical Society
2010
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| Online Access: | http://hdl.handle.net/1721.1/52548 https://orcid.org/0000-0002-4911-3183 |
| _version_ | 1811080474334855168 |
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| author | Iqbal, Nabil Liu, Hong |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Iqbal, Nabil Liu, Hong |
| author_sort | Iqbal, Nabil |
| collection | MIT |
| description | We show that at the level of linear response the low-frequency limit of a strongly coupled field theory at finite temperature is determined by the horizon geometry of its gravity dual, i.e., by the “membrane paradigm” fluid of classical black hole mechanics. Thus, generic boundary theory transport coefficients can be expressed in terms of geometric quantities evaluated at the horizon. When applied to the stress tensor this gives a simple, general proof of the universality of the shear viscosity in terms of the universality of gravitational couplings, and when applied to a conserved current it gives a new general formula for the conductivity. Away from the low-frequency limit the behavior of the boundary theory fluid is no longer fully captured by the horizon fluid even within the derivative expansion; instead, we find a nontrivial evolution from the horizon to the boundary. We derive flow equations governing this evolution and apply them to the simple examples of charge and momentum diffusio |
| first_indexed | 2024-09-23T11:31:57Z |
| format | Article |
| id | mit-1721.1/52548 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:31:57Z |
| publishDate | 2010 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/525482022-09-27T20:10:10Z Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm Iqbal, Nabil Liu, Hong Massachusetts Institute of Technology. Center for Theoretical Physics Massachusetts Institute of Technology. Department of Physics Liu, Hong Iqbal, Nabil Liu, Hong We show that at the level of linear response the low-frequency limit of a strongly coupled field theory at finite temperature is determined by the horizon geometry of its gravity dual, i.e., by the “membrane paradigm” fluid of classical black hole mechanics. Thus, generic boundary theory transport coefficients can be expressed in terms of geometric quantities evaluated at the horizon. When applied to the stress tensor this gives a simple, general proof of the universality of the shear viscosity in terms of the universality of gravitational couplings, and when applied to a conserved current it gives a new general formula for the conductivity. Away from the low-frequency limit the behavior of the boundary theory fluid is no longer fully captured by the horizon fluid even within the derivative expansion; instead, we find a nontrivial evolution from the horizon to the boundary. We derive flow equations governing this evolution and apply them to the simple examples of charge and momentum diffusio Department of Energy (Contract No. DF-FC02-94ER40818) 2010-03-12T18:53:36Z 2010-03-12T18:53:36Z 2009-01 2008-12 Article http://purl.org/eprint/type/JournalArticle 1550-2368 1550-7998 http://hdl.handle.net/1721.1/52548 Iqbal, Nabil , and Hong Liu. “Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm.” Physical Review D 79.2 (2009): 025023. © 2009 The American Physical Society https://orcid.org/0000-0002-4911-3183 en_US http://dx.doi.org/10.1103/PhysRevD.79.025023 Physical Review D Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society APS |
| spellingShingle | Iqbal, Nabil Liu, Hong Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm |
| title | Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm |
| title_full | Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm |
| title_fullStr | Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm |
| title_full_unstemmed | Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm |
| title_short | Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm |
| title_sort | universality of the hydrodynamic limit in ads cft and the membrane paradigm |
| url | http://hdl.handle.net/1721.1/52548 https://orcid.org/0000-0002-4911-3183 |
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