Crossing symmetry in alpha space
Abstract We initiate the study of the conformal bootstrap using Sturm-Liouville theory, specializing to four-point functions in one-dimensional CFTs. We do so by decomposing conformal correlators using a basis of eigenfunctions of the Casimir which are labeled by a complex number α. This leads to a...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-11-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP11(2017)193 |
| _version_ | 1818849981422895104 |
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| author | Matthijs Hogervorst Balt C. van Rees |
| author_facet | Matthijs Hogervorst Balt C. van Rees |
| author_sort | Matthijs Hogervorst |
| collection | DOAJ |
| description | Abstract We initiate the study of the conformal bootstrap using Sturm-Liouville theory, specializing to four-point functions in one-dimensional CFTs. We do so by decomposing conformal correlators using a basis of eigenfunctions of the Casimir which are labeled by a complex number α. This leads to a systematic method for computing conformal block decompositions. Analyzing bootstrap equations in alpha space turns crossing symmetry into an eigenvalue problem for an integral operator K. The operator K is closely related to the Wilson transform, and some of its eigenfunctions can be found in closed form. |
| first_indexed | 2024-12-19T06:41:52Z |
| format | Article |
| id | doaj.art-ecac1cb5edc248f59819728586aee95f |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-19T06:41:52Z |
| publishDate | 2017-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-ecac1cb5edc248f59819728586aee95f2022-12-21T20:32:02ZengSpringerOpenJournal of High Energy Physics1029-84792017-11-0120171114310.1007/JHEP11(2017)193Crossing symmetry in alpha spaceMatthijs Hogervorst0Balt C. van Rees1C.N. Yang Institute for Theoretical Physics, Stony Brook UniversityCentre for Particle Theory & Department of Mathematical Sciences, Durham UniversityAbstract We initiate the study of the conformal bootstrap using Sturm-Liouville theory, specializing to four-point functions in one-dimensional CFTs. We do so by decomposing conformal correlators using a basis of eigenfunctions of the Casimir which are labeled by a complex number α. This leads to a systematic method for computing conformal block decompositions. Analyzing bootstrap equations in alpha space turns crossing symmetry into an eigenvalue problem for an integral operator K. The operator K is closely related to the Wilson transform, and some of its eigenfunctions can be found in closed form.http://link.springer.com/article/10.1007/JHEP11(2017)193Conformal Field TheoryField Theories in Lower Dimensions |
| spellingShingle | Matthijs Hogervorst Balt C. van Rees Crossing symmetry in alpha space Journal of High Energy Physics Conformal Field Theory Field Theories in Lower Dimensions |
| title | Crossing symmetry in alpha space |
| title_full | Crossing symmetry in alpha space |
| title_fullStr | Crossing symmetry in alpha space |
| title_full_unstemmed | Crossing symmetry in alpha space |
| title_short | Crossing symmetry in alpha space |
| title_sort | crossing symmetry in alpha space |
| topic | Conformal Field Theory Field Theories in Lower Dimensions |
| url | http://link.springer.com/article/10.1007/JHEP11(2017)193 |
| work_keys_str_mv | AT matthijshogervorst crossingsymmetryinalphaspace AT baltcvanrees crossingsymmetryinalphaspace |