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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Autores principales:	Ilija Burić, Sylvain Lacroix, Jeremy Mann, Lorenzo Quintavalle, Volker Schomerus
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Conformal Field Theory Space-Time Symmetries Differential and Algebraic Geometry Integrable Hierarchies Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
Acceso en línea:	https://doaj.org/article/a4a8ab1a4b5245bba0eb72703e7066b9
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spelling	oai:doaj.org-article:a4a8ab1a4b5245bba0eb72703e7066b92021-11-28T12:40:37ZGaudin models and multipoint conformal blocks. Part II. Comb channel vertices in 3D and 4D10.1007/JHEP11(2021)1821029-8479https://doaj.org/article/a4a8ab1a4b5245bba0eb72703e7066b92021-11-01T00:00:00Zhttps://doi.org/10.1007/JHEP11(2021)182https://doaj.org/toc/1029-8479Abstract 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.Ilija BurićSylvain LacroixJeremy MannLorenzo QuintavalleVolker SchomerusSpringerOpenarticleConformal Field TheorySpace-Time SymmetriesDifferential and Algebraic GeometryIntegrable HierarchiesNuclear and particle physics. Atomic energy. RadioactivityQC770-798ENJournal of High Energy Physics, Vol 2021, Iss 11, Pp 1-69 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Conformal Field Theory Space-Time Symmetries Differential and Algebraic Geometry Integrable Hierarchies Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
spellingShingle	Conformal Field Theory Space-Time Symmetries Differential and Algebraic Geometry Integrable Hierarchies Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 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
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.
format	article
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
title	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_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_sort	gaudin models and multipoint conformal blocks. part ii. comb channel vertices in 3d and 4d
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/a4a8ab1a4b5245bba0eb72703e7066b9
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Gaudin models and multipoint conformal blocks. Part II. Comb channel vertices in 3D and 4D

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