Universal spinning Casimir equations and their solutions
Abstract Conformal blocks are a central analytic tool for higher dimensional conformal field theory. We employ Harish-Chandra’s radial component map to construct universal Casimir differential equations for spinning conformal blocks in any dimension d of Euclidean space. Furthermore, we also build a...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-03-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP03(2023)133 |
| _version_ | 1827917204556873728 |
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| author | Ilija Burić Volker Schomerus |
| author_facet | Ilija Burić Volker Schomerus |
| author_sort | Ilija Burić |
| collection | DOAJ |
| description | Abstract Conformal blocks are a central analytic tool for higher dimensional conformal field theory. We employ Harish-Chandra’s radial component map to construct universal Casimir differential equations for spinning conformal blocks in any dimension d of Euclidean space. Furthermore, we also build a set of differential “shifting” operators that allow to construct solutions of the Casimir equations from certain seeds. In the context of spinning four-point blocks of bulk conformal field theory, our formulas provide an elegant and far reaching generalisation of existing expressions to arbitrary tensor fields and arbitrary dimension d. The power of our new universal approach to spinning blocks is further illustrated through applications to defect conformal field theory. In the case of defects of co-dimension q = 2 we are able to construct conformal blocks for two-point functions of symmetric traceless bulk tensor fields in both the defect and the bulk channel. This opens an interesting avenue for applications to the defect bootstrap. Finally, we also derive the Casimir equations for bulk-bulk-defect three-point functions in the bulk channel. |
| first_indexed | 2024-03-13T03:25:30Z |
| format | Article |
| id | doaj.art-b35d6ac47b7c429f847bbb7f287b6bf1 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-13T03:25:30Z |
| publishDate | 2023-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-b35d6ac47b7c429f847bbb7f287b6bf12023-06-25T11:06:08ZengSpringerOpenJournal of High Energy Physics1029-84792023-03-012023316610.1007/JHEP03(2023)133Universal spinning Casimir equations and their solutionsIlija Burić0Volker Schomerus1Department of Physics, University of PisaDeutsches Elektronen Synchroton DESYAbstract Conformal blocks are a central analytic tool for higher dimensional conformal field theory. We employ Harish-Chandra’s radial component map to construct universal Casimir differential equations for spinning conformal blocks in any dimension d of Euclidean space. Furthermore, we also build a set of differential “shifting” operators that allow to construct solutions of the Casimir equations from certain seeds. In the context of spinning four-point blocks of bulk conformal field theory, our formulas provide an elegant and far reaching generalisation of existing expressions to arbitrary tensor fields and arbitrary dimension d. The power of our new universal approach to spinning blocks is further illustrated through applications to defect conformal field theory. In the case of defects of co-dimension q = 2 we are able to construct conformal blocks for two-point functions of symmetric traceless bulk tensor fields in both the defect and the bulk channel. This opens an interesting avenue for applications to the defect bootstrap. Finally, we also derive the Casimir equations for bulk-bulk-defect three-point functions in the bulk channel.https://doi.org/10.1007/JHEP03(2023)133Scale and Conformal SymmetriesField Theories in Higher DimensionsIntegrable Hierarchies |
| spellingShingle | Ilija Burić Volker Schomerus Universal spinning Casimir equations and their solutions Journal of High Energy Physics Scale and Conformal Symmetries Field Theories in Higher Dimensions Integrable Hierarchies |
| title | Universal spinning Casimir equations and their solutions |
| title_full | Universal spinning Casimir equations and their solutions |
| title_fullStr | Universal spinning Casimir equations and their solutions |
| title_full_unstemmed | Universal spinning Casimir equations and their solutions |
| title_short | Universal spinning Casimir equations and their solutions |
| title_sort | universal spinning casimir equations and their solutions |
| topic | Scale and Conformal Symmetries Field Theories in Higher Dimensions Integrable Hierarchies |
| url | https://doi.org/10.1007/JHEP03(2023)133 |
| work_keys_str_mv | AT ilijaburic universalspinningcasimirequationsandtheirsolutions AT volkerschomerus universalspinningcasimirequationsandtheirsolutions |