Gaudin models and multipoint conformal blocks. Part II. Comb channel vertices in 3D and 4D
Abstract It was recently shown that multi-point conformal blocks in higher dimensional conformal field theory can be considered as joint eigenfunctions for a system of commuting differential operators. The latter arise as Hamiltonians of a Gaudin integrable system. In this work we address the reduce...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-11-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP11(2021)182 |
| _version_ | 1819014966259220480 |
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| author | Ilija Burić Sylvain Lacroix Jeremy Mann Lorenzo Quintavalle Volker Schomerus |
| author_facet | Ilija Burić Sylvain Lacroix Jeremy Mann Lorenzo Quintavalle Volker Schomerus |
| author_sort | Ilija Burić |
| collection | DOAJ |
| description | Abstract It was recently shown that multi-point conformal blocks in higher dimensional conformal field theory can be considered as joint eigenfunctions for a system of commuting differential operators. The latter arise as Hamiltonians of a Gaudin integrable system. In this work we address the reduced fourth order differential operators that measure the choice of 3-point tensor structures for all vertices of 3- and 4-dimensional comb channel conformal blocks. These vertices come associated with a single cross ratio. Remarkably, we identify the vertex operators as Hamiltonians of a crystallographic elliptic Calogero-Moser-Sutherland model that was discovered originally by Etingof, Felder, Ma and Veselov. Our construction is based on a further development of the embedding space formalism for mixed-symmetry tensor fields. The results thereby also apply to comb channel vertices of 5- and 6-point functions in arbitrary dimension. |
| first_indexed | 2024-12-21T02:24:14Z |
| format | Article |
| id | doaj.art-a4a8ab1a4b5245bba0eb72703e7066b9 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-21T02:24:14Z |
| publishDate | 2021-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-a4a8ab1a4b5245bba0eb72703e7066b92022-12-21T19:19:02ZengSpringerOpenJournal of High Energy Physics1029-84792021-11-0120211116910.1007/JHEP11(2021)182Gaudin models and multipoint conformal blocks. Part II. Comb channel vertices in 3D and 4DIlija Burić0Sylvain Lacroix1Jeremy Mann2Lorenzo Quintavalle3Volker Schomerus4DESY Theory Group, DESY HamburgII. Institut für Theoretische Physik, Universität HamburgDESY Theory Group, DESY HamburgDESY Theory Group, DESY HamburgDESY Theory Group, DESY HamburgAbstract It was recently shown that multi-point conformal blocks in higher dimensional conformal field theory can be considered as joint eigenfunctions for a system of commuting differential operators. The latter arise as Hamiltonians of a Gaudin integrable system. In this work we address the reduced fourth order differential operators that measure the choice of 3-point tensor structures for all vertices of 3- and 4-dimensional comb channel conformal blocks. These vertices come associated with a single cross ratio. Remarkably, we identify the vertex operators as Hamiltonians of a crystallographic elliptic Calogero-Moser-Sutherland model that was discovered originally by Etingof, Felder, Ma and Veselov. Our construction is based on a further development of the embedding space formalism for mixed-symmetry tensor fields. The results thereby also apply to comb channel vertices of 5- and 6-point functions in arbitrary dimension.https://doi.org/10.1007/JHEP11(2021)182Conformal Field TheorySpace-Time SymmetriesDifferential and Algebraic GeometryIntegrable Hierarchies |
| spellingShingle | Ilija Burić Sylvain Lacroix Jeremy Mann Lorenzo Quintavalle Volker Schomerus Gaudin models and multipoint conformal blocks. Part II. Comb channel vertices in 3D and 4D Journal of High Energy Physics Conformal Field Theory Space-Time Symmetries Differential and Algebraic Geometry Integrable Hierarchies |
| title | Gaudin models and multipoint conformal blocks. Part II. Comb channel vertices in 3D and 4D |
| title_full | Gaudin models and multipoint conformal blocks. Part II. Comb channel vertices in 3D and 4D |
| title_fullStr | Gaudin models and multipoint conformal blocks. Part II. Comb channel vertices in 3D and 4D |
| title_full_unstemmed | Gaudin models and multipoint conformal blocks. Part II. Comb channel vertices in 3D and 4D |
| title_short | Gaudin models and multipoint conformal blocks. Part II. Comb channel vertices in 3D and 4D |
| title_sort | gaudin models and multipoint conformal blocks part ii comb channel vertices in 3d and 4d |
| topic | Conformal Field Theory Space-Time Symmetries Differential and Algebraic Geometry Integrable Hierarchies |
| url | https://doi.org/10.1007/JHEP11(2021)182 |
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