Effective action for relativistic hydrodynamics: fluctuations, dissipation, and entropy inflow
Abstract We present a detailed and self-contained analysis of the universal SchwingerKeldysh effective field theory which describes macroscopic thermal fluctuations of a relativistic field theory, elaborating on our earlier construction [1]. We write an effective action for appropriate hydrodynamic...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-10-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP10(2018)194 |
| _version_ | 1818560621056098304 |
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| author | Felix M. Haehl R. Loganayagam Mukund Rangamani |
| author_facet | Felix M. Haehl R. Loganayagam Mukund Rangamani |
| author_sort | Felix M. Haehl |
| collection | DOAJ |
| description | Abstract We present a detailed and self-contained analysis of the universal SchwingerKeldysh effective field theory which describes macroscopic thermal fluctuations of a relativistic field theory, elaborating on our earlier construction [1]. We write an effective action for appropriate hydrodynamic Goldstone modes and fluctuation fields, and discuss the symmetries to be imposed. The constraints imposed by fluctuation-dissipation theorem are manifest in our formalism. Consequently, the action reproduces hydrodynamic constitutive relations consistent with the local second law at all orders in the derivative expansion, and captures the essential elements of the eightfold classification of hydrodynamic transport of [2]. We demonstrate how to recover the hydrodynamic entropy and give predictions for the non-Gaussian hydrodynamic fluctuations. The basic ingredients of our construction involve (i) doubling of degrees of freedom a la Schwinger-Keldysh, (ii) an emergent gauge U(1)T symmetry associated with entropy which is encapsulated in a Noether current a la Wald, and (iii) a BRST/topological supersymmetry imposing the fluctuation-dissipation theorem a la Parisi-Sourlas. The overarching mathematical framework for our construction is provided by the balanced equivariant cohomology of thermal translations, which captures the basic constraints arising from the Schwinger-Keldysh doubling, and the thermal Kubo-Martin-Schwinger relations. All these features are conveniently implemented in a covariant superspace formalism. An added benefit is that the second law can be understood as being due to entropy inflow from the Grassmann-odd directions of superspace. |
| first_indexed | 2024-12-14T00:40:38Z |
| format | Article |
| id | doaj.art-9de27aa503d74a0687efdee9d92a62ca |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-14T00:40:38Z |
| publishDate | 2018-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-9de27aa503d74a0687efdee9d92a62ca2022-12-21T23:24:24ZengSpringerOpenJournal of High Energy Physics1029-84792018-10-01201810111610.1007/JHEP10(2018)194Effective action for relativistic hydrodynamics: fluctuations, dissipation, and entropy inflowFelix M. Haehl0R. Loganayagam1Mukund Rangamani2Department of Physics and Astronomy, University of British ColumbiaInternational Centre for Theoretical Sciences (ICTS-TIFR)Center for Quantum Mathematics and Physics (QMAP), Department of Physics, University of CaliforniaAbstract We present a detailed and self-contained analysis of the universal SchwingerKeldysh effective field theory which describes macroscopic thermal fluctuations of a relativistic field theory, elaborating on our earlier construction [1]. We write an effective action for appropriate hydrodynamic Goldstone modes and fluctuation fields, and discuss the symmetries to be imposed. The constraints imposed by fluctuation-dissipation theorem are manifest in our formalism. Consequently, the action reproduces hydrodynamic constitutive relations consistent with the local second law at all orders in the derivative expansion, and captures the essential elements of the eightfold classification of hydrodynamic transport of [2]. We demonstrate how to recover the hydrodynamic entropy and give predictions for the non-Gaussian hydrodynamic fluctuations. The basic ingredients of our construction involve (i) doubling of degrees of freedom a la Schwinger-Keldysh, (ii) an emergent gauge U(1)T symmetry associated with entropy which is encapsulated in a Noether current a la Wald, and (iii) a BRST/topological supersymmetry imposing the fluctuation-dissipation theorem a la Parisi-Sourlas. The overarching mathematical framework for our construction is provided by the balanced equivariant cohomology of thermal translations, which captures the basic constraints arising from the Schwinger-Keldysh doubling, and the thermal Kubo-Martin-Schwinger relations. All these features are conveniently implemented in a covariant superspace formalism. An added benefit is that the second law can be understood as being due to entropy inflow from the Grassmann-odd directions of superspace.http://link.springer.com/article/10.1007/JHEP10(2018)194Effective Field TheoriesTopological Field TheoriesQuantum Dissipative SystemsAdS-CFT Correspondence |
| spellingShingle | Felix M. Haehl R. Loganayagam Mukund Rangamani Effective action for relativistic hydrodynamics: fluctuations, dissipation, and entropy inflow Journal of High Energy Physics Effective Field Theories Topological Field Theories Quantum Dissipative Systems AdS-CFT Correspondence |
| title | Effective action for relativistic hydrodynamics: fluctuations, dissipation, and entropy inflow |
| title_full | Effective action for relativistic hydrodynamics: fluctuations, dissipation, and entropy inflow |
| title_fullStr | Effective action for relativistic hydrodynamics: fluctuations, dissipation, and entropy inflow |
| title_full_unstemmed | Effective action for relativistic hydrodynamics: fluctuations, dissipation, and entropy inflow |
| title_short | Effective action for relativistic hydrodynamics: fluctuations, dissipation, and entropy inflow |
| title_sort | effective action for relativistic hydrodynamics fluctuations dissipation and entropy inflow |
| topic | Effective Field Theories Topological Field Theories Quantum Dissipative Systems AdS-CFT Correspondence |
| url | http://link.springer.com/article/10.1007/JHEP10(2018)194 |
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