Efficient rules for all conformal blocks

Abstract We formulate a set of general rules for computing d-dimensional four-point global conformal blocks of operators in arbitrary Lorentz representations in the context of the embedding space operator product expansion formalism [1]. With these rules, the procedure for determining any conformal...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Jean-François Fortin, Wen-Jie Ma, Valentina Prilepina, Witold Skiba
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Conformal Field Theory Conformal and W Symmetry Field Theories in Higher Dimensions Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
Acceso en línea:	https://doaj.org/article/7b712ccefc4140aebec2a11ec0cf617b
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:7b712ccefc4140aebec2a11ec0cf617b
record_format	dspace
spelling	oai:doaj.org-article:7b712ccefc4140aebec2a11ec0cf617b2021-11-14T12:40:52ZEfficient rules for all conformal blocks10.1007/JHEP11(2021)0521029-8479https://doaj.org/article/7b712ccefc4140aebec2a11ec0cf617b2021-11-01T00:00:00Zhttps://doi.org/10.1007/JHEP11(2021)052https://doaj.org/toc/1029-8479Abstract We formulate a set of general rules for computing d-dimensional four-point global conformal blocks of operators in arbitrary Lorentz representations in the context of the embedding space operator product expansion formalism [1]. With these rules, the procedure for determining any conformal block of interest is reduced to (1) identifying the relevant projection operators and tensor structures and (2) applying the conformal rules to obtain the blocks. To facilitate the bookkeeping of contributing terms, we introduce a convenient diagrammatic notation. We present several concrete examples to illustrate the general procedure as well as to demonstrate and test the explicit application of the rules. In particular, we consider four-point functions involving scalars S and some specific irreducible representations R, namely 〈SSSS〉, 〈SSSR〉, 〈SRSR〉 and 〈SSRR〉 (where, when allowed, R is a vector or a fermion), and determine the corresponding blocks for all possible exchanged representations.Jean-François FortinWen-Jie MaValentina PrilepinaWitold SkibaSpringerOpenarticleConformal Field TheoryConformal and W SymmetryField Theories inHigher DimensionsNuclear and particle physics. Atomic energy. RadioactivityQC770-798ENJournal of High Energy Physics, Vol 2021, Iss 11, Pp 1-61 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Conformal Field Theory Conformal and W Symmetry Field Theories in Higher Dimensions Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
spellingShingle	Conformal Field Theory Conformal and W Symmetry Field Theories in Higher Dimensions Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 Jean-François Fortin Wen-Jie Ma Valentina Prilepina Witold Skiba Efficient rules for all conformal blocks
description	Abstract We formulate a set of general rules for computing d-dimensional four-point global conformal blocks of operators in arbitrary Lorentz representations in the context of the embedding space operator product expansion formalism [1]. With these rules, the procedure for determining any conformal block of interest is reduced to (1) identifying the relevant projection operators and tensor structures and (2) applying the conformal rules to obtain the blocks. To facilitate the bookkeeping of contributing terms, we introduce a convenient diagrammatic notation. We present several concrete examples to illustrate the general procedure as well as to demonstrate and test the explicit application of the rules. In particular, we consider four-point functions involving scalars S and some specific irreducible representations R, namely 〈SSSS〉, 〈SSSR〉, 〈SRSR〉 and 〈SSRR〉 (where, when allowed, R is a vector or a fermion), and determine the corresponding blocks for all possible exchanged representations.
format	article
author	Jean-François Fortin Wen-Jie Ma Valentina Prilepina Witold Skiba
author_facet	Jean-François Fortin Wen-Jie Ma Valentina Prilepina Witold Skiba
author_sort	Jean-François Fortin
title	Efficient rules for all conformal blocks
title_short	Efficient rules for all conformal blocks
title_full	Efficient rules for all conformal blocks
title_fullStr	Efficient rules for all conformal blocks
title_full_unstemmed	Efficient rules for all conformal blocks
title_sort	efficient rules for all conformal blocks
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/7b712ccefc4140aebec2a11ec0cf617b
work_keys_str_mv	AT jeanfrancoisfortin efficientrulesforallconformalblocks AT wenjiema efficientrulesforallconformalblocks AT valentinaprilepina efficientrulesforallconformalblocks AT witoldskiba efficientrulesforallconformalblocks
_version_	1718429114936852480

Efficient rules for all conformal blocks

Ejemplares similares