Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory
Abstract Conformal blocks are the central ingredient of the conformal bootstrap programme. We elaborate on our recent observation that uncovered a relation with wave functions of an integrable Calogero-Sutherland Hamiltonian in order to develop a systematic theory of conformal blocks. Our main goal...
Main Authors: | , |
---|---|
Format: | Article |
Language: | English |
Published: |
SpringerOpen
2018-07-01
|
Series: | Journal of High Energy Physics |
Subjects: | |
Online Access: | http://link.springer.com/article/10.1007/JHEP07(2018)180 |
id |
doaj-77845b87062641c9a2c0ea8273048fc6 |
---|---|
record_format |
Article |
spelling |
doaj-77845b87062641c9a2c0ea8273048fc62020-11-25T02:03:06ZengSpringerOpenJournal of High Energy Physics1029-84792018-07-012018716610.1007/JHEP07(2018)180Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theoryMikhail Isachenkov0Volker Schomerus1Department of Particle Physics and Astrophysics, Weizmann Institute of ScienceDESY Theory Group, DESY HamburgAbstract Conformal blocks are the central ingredient of the conformal bootstrap programme. We elaborate on our recent observation that uncovered a relation with wave functions of an integrable Calogero-Sutherland Hamiltonian in order to develop a systematic theory of conformal blocks. Our main goal here is to review central ingredients of the Heckman-Opdam theory for scattering states of Calogero-Sutherland models with special emphasis to the relation with scalar 4-point blocks. We will also discuss a number of direct consequences for conformal blocks, including a new series expansion for blocks of arbitrary complex spin and a complete analysis of their poles and residues. Applications to the Froissart-Gribov formula for conformal field theory, as well as extensions to spinning blocks and defects are briefly discussed before we conclude with an outlook on forthcoming work concerning algebraic consequences of integrability.http://link.springer.com/article/10.1007/JHEP07(2018)180Conformal and W SymmetryConformal Field TheoryField Theories in Higher Dimensions |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Mikhail Isachenkov Volker Schomerus |
spellingShingle |
Mikhail Isachenkov Volker Schomerus Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory Journal of High Energy Physics Conformal and W Symmetry Conformal Field Theory Field Theories in Higher Dimensions |
author_facet |
Mikhail Isachenkov Volker Schomerus |
author_sort |
Mikhail Isachenkov |
title |
Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory |
title_short |
Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory |
title_full |
Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory |
title_fullStr |
Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory |
title_full_unstemmed |
Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory |
title_sort |
integrability of conformal blocks. part i. calogero-sutherland scattering theory |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2018-07-01 |
description |
Abstract Conformal blocks are the central ingredient of the conformal bootstrap programme. We elaborate on our recent observation that uncovered a relation with wave functions of an integrable Calogero-Sutherland Hamiltonian in order to develop a systematic theory of conformal blocks. Our main goal here is to review central ingredients of the Heckman-Opdam theory for scattering states of Calogero-Sutherland models with special emphasis to the relation with scalar 4-point blocks. We will also discuss a number of direct consequences for conformal blocks, including a new series expansion for blocks of arbitrary complex spin and a complete analysis of their poles and residues. Applications to the Froissart-Gribov formula for conformal field theory, as well as extensions to spinning blocks and defects are briefly discussed before we conclude with an outlook on forthcoming work concerning algebraic consequences of integrability. |
topic |
Conformal and W Symmetry Conformal Field Theory Field Theories in Higher Dimensions |
url |
http://link.springer.com/article/10.1007/JHEP07(2018)180 |
work_keys_str_mv |
AT mikhailisachenkov integrabilityofconformalblocksparticalogerosutherlandscatteringtheory AT volkerschomerus integrabilityofconformalblocksparticalogerosutherlandscatteringtheory |
_version_ |
1724949522021351424 |