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...
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| Main Authors: | , , , , |
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| Format: | article |
| Language: | EN |
| Published: |
SpringerOpen
2021
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| Subjects: | |
| Online Access: | https://doaj.org/article/a4a8ab1a4b5245bba0eb72703e7066b9 |
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| Summary: | 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. |
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