Diagonal Limit for Conformal Blocks in d Dimensions

Conformal blocks in any number of dimensions depend on two variables z, zbar. Here we study their restrictions to the special "diagonal" kinematics z = zbar, previously found useful as a starting point for the conformal bootstrap analysis. We show that conformal blocks on the diagonal sati...

Descripción completa

Detalles Bibliográficos
Autores principales: Hogervorst, Matthijs, Osborn, Hugh, Rychkov, Slava
Lenguaje:eng
Publicado: 2013
Materias:
Particle Physics - Theory
Acceso en línea:https://dx.doi.org/10.1007/JHEP08(2013)014
http://cds.cern.ch/record/1546083
_version_ 1780930097444814848
author Hogervorst, Matthijs
Osborn, Hugh
Rychkov, Slava
author_facet Hogervorst, Matthijs
Osborn, Hugh
Rychkov, Slava
author_sort Hogervorst, Matthijs
collection CERN
description Conformal blocks in any number of dimensions depend on two variables z, zbar. Here we study their restrictions to the special "diagonal" kinematics z = zbar, previously found useful as a starting point for the conformal bootstrap analysis. We show that conformal blocks on the diagonal satisfy ordinary differential equations, third-order for spin zero and fourth-order for the general case. These ODEs determine the blocks uniquely and lead to an efficient numerical evaluation algorithm. For equal external operator dimensions, we find closed-form solutions in terms of finite sums of 3F2 functions.
id cern-1546083
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2013
record_format invenio
spelling cern-15460832023-10-04T08:49:00Zdoi:10.1007/JHEP08(2013)014http://cds.cern.ch/record/1546083engHogervorst, MatthijsOsborn, HughRychkov, SlavaDiagonal Limit for Conformal Blocks in d DimensionsParticle Physics - TheoryConformal blocks in any number of dimensions depend on two variables z, zbar. Here we study their restrictions to the special "diagonal" kinematics z = zbar, previously found useful as a starting point for the conformal bootstrap analysis. We show that conformal blocks on the diagonal satisfy ordinary differential equations, third-order for spin zero and fourth-order for the general case. These ODEs determine the blocks uniquely and lead to an efficient numerical evaluation algorithm. For equal external operator dimensions, we find closed-form solutions in terms of finite sums of 3F2 functions.Conformal blocks in any number of dimensions depend on two variables z, . Here we study their restrictions to the special “diagonal” kinematics , previously found useful as a starting point for the conformal bootstrap analysis. We show that conformal blocks on the diagonal satisfy ordinary differential equations, third-order for spin zero and fourth-order for the general case. These ODEs determine the blocks uniquely and lead to an efficient numerical evaluation algorithm. For equal external operator dimensions, we find closed-form solutions in terms of finite sums of (3) F (2) functions.Conformal blocks in any number of dimensions depend on two variables z, zbar. Here we study their restrictions to the special "diagonal" kinematics z = zbar, previously found useful as a starting point for the conformal bootstrap analysis. We show that conformal blocks on the diagonal satisfy ordinary differential equations, third-order for spin zero and fourth-order for the general case. These ODEs determine the blocks uniquely and lead to an efficient numerical evaluation algorithm. For equal external operator dimensions, we find closed-form solutions in terms of finite sums of 3F2 functions.arXiv:1305.1321LPTENS-13-10CERN-PH-TH-2013-092DAMTP-2013-16DAMTP-2013-16LPTENS-13-10CERN-PH-TH-2013-092oai:cds.cern.ch:15460832013-05-08
spellingShingle Particle Physics - Theory
Hogervorst, Matthijs
Osborn, Hugh
Rychkov, Slava
Diagonal Limit for Conformal Blocks in d Dimensions
title Diagonal Limit for Conformal Blocks in d Dimensions
title_full Diagonal Limit for Conformal Blocks in d Dimensions
title_fullStr Diagonal Limit for Conformal Blocks in d Dimensions
title_full_unstemmed Diagonal Limit for Conformal Blocks in d Dimensions
title_short Diagonal Limit for Conformal Blocks in d Dimensions
title_sort diagonal limit for conformal blocks in d dimensions
topic Particle Physics - Theory
url https://dx.doi.org/10.1007/JHEP08(2013)014
http://cds.cern.ch/record/1546083
work_keys_str_mv AT hogervorstmatthijs diagonallimitforconformalblocksinddimensions
AT osbornhugh diagonallimitforconformalblocksinddimensions
AT rychkovslava diagonallimitforconformalblocksinddimensions

Ejemplares similares