Spontaneous symmetry breaking, conformal anomaly and incompressible fluid turbulence
Abstract We propose an effective conformal field theory (CFT) description of steady state incompressible fluid turbulence at the inertial range of scales in any number of spatial dimensions. We derive a KPZ-type equation for the anomalous scaling of the longitudinal velocity structure functions and...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-11-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP11(2017)040 |
| _version_ | 1819096585359851520 |
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| author | Yaron Oz |
| author_facet | Yaron Oz |
| author_sort | Yaron Oz |
| collection | DOAJ |
| description | Abstract We propose an effective conformal field theory (CFT) description of steady state incompressible fluid turbulence at the inertial range of scales in any number of spatial dimensions. We derive a KPZ-type equation for the anomalous scaling of the longitudinal velocity structure functions and relate the intermittency parameter to the boundary Euler (A-type) conformal anomaly coefficient. The proposed theory consists of a mean field CFT that exhibits Kolmogorov linear scaling (K41 theory) coupled to a dilaton. The dilaton is a Nambu-Goldstone gapless mode that arises from a spontaneous breaking due to the energy flux of the separate scale and time symmetries of the inviscid Navier-Stokes equations to a K41 scaling with a dynamical exponent z=23 $$ z=\frac{2}{3} $$. The dilaton acts as a random measure that dresses the K41 theory and introduces intermittency. We discuss the two, three and large number of space dimensions cases and how entanglement entropy can be used to characterize the intermittency strength. |
| first_indexed | 2024-12-22T00:01:32Z |
| format | Article |
| id | doaj.art-8c58715936f84f69859b18536485ca96 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-22T00:01:32Z |
| publishDate | 2017-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-8c58715936f84f69859b18536485ca962022-12-21T18:45:42ZengSpringerOpenJournal of High Energy Physics1029-84792017-11-0120171112210.1007/JHEP11(2017)040Spontaneous symmetry breaking, conformal anomaly and incompressible fluid turbulenceYaron Oz0Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv UniversityAbstract We propose an effective conformal field theory (CFT) description of steady state incompressible fluid turbulence at the inertial range of scales in any number of spatial dimensions. We derive a KPZ-type equation for the anomalous scaling of the longitudinal velocity structure functions and relate the intermittency parameter to the boundary Euler (A-type) conformal anomaly coefficient. The proposed theory consists of a mean field CFT that exhibits Kolmogorov linear scaling (K41 theory) coupled to a dilaton. The dilaton is a Nambu-Goldstone gapless mode that arises from a spontaneous breaking due to the energy flux of the separate scale and time symmetries of the inviscid Navier-Stokes equations to a K41 scaling with a dynamical exponent z=23 $$ z=\frac{2}{3} $$. The dilaton acts as a random measure that dresses the K41 theory and introduces intermittency. We discuss the two, three and large number of space dimensions cases and how entanglement entropy can be used to characterize the intermittency strength.http://link.springer.com/article/10.1007/JHEP11(2017)040Anomalies in Field and String TheoriesBoundary Quantum Field TheoryConformal Field TheoryRandom Systems |
| spellingShingle | Yaron Oz Spontaneous symmetry breaking, conformal anomaly and incompressible fluid turbulence Journal of High Energy Physics Anomalies in Field and String Theories Boundary Quantum Field Theory Conformal Field Theory Random Systems |
| title | Spontaneous symmetry breaking, conformal anomaly and incompressible fluid turbulence |
| title_full | Spontaneous symmetry breaking, conformal anomaly and incompressible fluid turbulence |
| title_fullStr | Spontaneous symmetry breaking, conformal anomaly and incompressible fluid turbulence |
| title_full_unstemmed | Spontaneous symmetry breaking, conformal anomaly and incompressible fluid turbulence |
| title_short | Spontaneous symmetry breaking, conformal anomaly and incompressible fluid turbulence |
| title_sort | spontaneous symmetry breaking conformal anomaly and incompressible fluid turbulence |
| topic | Anomalies in Field and String Theories Boundary Quantum Field Theory Conformal Field Theory Random Systems |
| url | http://link.springer.com/article/10.1007/JHEP11(2017)040 |
| work_keys_str_mv | AT yaronoz spontaneoussymmetrybreakingconformalanomalyandincompressiblefluidturbulence |