Zero modes of local operators in 2d CFT on a cylinder
Abstract Studies of Eigenstate Thermalization Hypothesis (ETH) in two-dimensional CFTs call for calculation of the expectation values of local operators in highly excited energy eigenstates. This can be done efficiently by representing zero modes of these operators in terms of the Virasoro algebra g...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-07-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP07(2020)172 |
| _version_ | 1818300444679602176 |
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| author | Anatoly Dymarsky Kirill Pavlenko Dmitry Solovyev |
| author_facet | Anatoly Dymarsky Kirill Pavlenko Dmitry Solovyev |
| author_sort | Anatoly Dymarsky |
| collection | DOAJ |
| description | Abstract Studies of Eigenstate Thermalization Hypothesis (ETH) in two-dimensional CFTs call for calculation of the expectation values of local operators in highly excited energy eigenstates. This can be done efficiently by representing zero modes of these operators in terms of the Virasoro algebra generators. In this paper we present a pedagogical introduction explaining how this calculation can be performed analytically or using computer algebra. We illustrate the computation of zero modes by a number of examples and list explicit expressions for all local operators from the vacuum family with the dimension of less or equal than eight. Finally, we derive an explicit expression for the quantum KdV generator Q 7 in terms of the Virasoro algebra generators. The obtained results can be used for quantitative studies of ETH at finite value of central charge. |
| first_indexed | 2024-12-13T05:07:13Z |
| format | Article |
| id | doaj.art-299b476de8994c9cbdf521998711250b |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-13T05:07:13Z |
| publishDate | 2020-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-299b476de8994c9cbdf521998711250b2022-12-21T23:58:37ZengSpringerOpenJournal of High Energy Physics1029-84792020-07-012020711810.1007/JHEP07(2020)172Zero modes of local operators in 2d CFT on a cylinderAnatoly Dymarsky0Kirill Pavlenko1Dmitry Solovyev2Department of Physics and Astronomy, University of KentuckySkolkovo Institute of Science and Technology, Skolkovo Innovation CenterDepartment of Physics, Saint Petersburg State UniversityAbstract Studies of Eigenstate Thermalization Hypothesis (ETH) in two-dimensional CFTs call for calculation of the expectation values of local operators in highly excited energy eigenstates. This can be done efficiently by representing zero modes of these operators in terms of the Virasoro algebra generators. In this paper we present a pedagogical introduction explaining how this calculation can be performed analytically or using computer algebra. We illustrate the computation of zero modes by a number of examples and list explicit expressions for all local operators from the vacuum family with the dimension of less or equal than eight. Finally, we derive an explicit expression for the quantum KdV generator Q 7 in terms of the Virasoro algebra generators. The obtained results can be used for quantitative studies of ETH at finite value of central charge.http://link.springer.com/article/10.1007/JHEP07(2020)172Conformal Field TheoryConformal and W SymmetryIntegrable Field The- ories |
| spellingShingle | Anatoly Dymarsky Kirill Pavlenko Dmitry Solovyev Zero modes of local operators in 2d CFT on a cylinder Journal of High Energy Physics Conformal Field Theory Conformal and W Symmetry Integrable Field The- ories |
| title | Zero modes of local operators in 2d CFT on a cylinder |
| title_full | Zero modes of local operators in 2d CFT on a cylinder |
| title_fullStr | Zero modes of local operators in 2d CFT on a cylinder |
| title_full_unstemmed | Zero modes of local operators in 2d CFT on a cylinder |
| title_short | Zero modes of local operators in 2d CFT on a cylinder |
| title_sort | zero modes of local operators in 2d cft on a cylinder |
| topic | Conformal Field Theory Conformal and W Symmetry Integrable Field The- ories |
| url | http://link.springer.com/article/10.1007/JHEP07(2020)172 |
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