One- and two-dimensional higher-point conformal blocks as free-particle wavefunctions in AdS 3 ⊗ m $$ {\textrm{AdS}}_3^{\otimes m} $$
Abstract We establish that all of the one- and two-dimensional global conformal blocks are, up to some choice of prefactor, free-particle wavefunctions in tensor products of AdS3 or limits thereof. Our first core observation is that the six-point comb-channel conformal blocks correspond to free-part...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-01-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP01(2024)031 |
| _version_ | 1797355989240905728 |
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| author | Jean-François Fortin Wen-Jie Ma Sarthak Parikh Lorenzo Quintavalle Witold Skiba |
| author_facet | Jean-François Fortin Wen-Jie Ma Sarthak Parikh Lorenzo Quintavalle Witold Skiba |
| author_sort | Jean-François Fortin |
| collection | DOAJ |
| description | Abstract We establish that all of the one- and two-dimensional global conformal blocks are, up to some choice of prefactor, free-particle wavefunctions in tensor products of AdS3 or limits thereof. Our first core observation is that the six-point comb-channel conformal blocks correspond to free-particle wavefunctions on an AdS3 constructed directly in cross-ratio space. This construction generalizes to blocks for a special class of diagrams, which are determined as free-particle wavefunctions in tensor products of AdS3. Conformal blocks for all the remaining topologies are obtained as limits of the free wavefunctions mentioned above. Our results show directly that the integrable models associated with all one- and two-dimensional conformal blocks can be seen as limits of free theory, and manifest a relation between AdS and CFT kinematics that lies outside of the standard AdS/CFT dictionary. We complete the discussion by providing explicit Feynman-like rules that can be used to work out blocks for all topologies, as well as a Mathematica notebook that allows simple computation of Casimir equations and series expansions for blocks, by requiring just an OPE diagram as input. |
| first_indexed | 2024-03-08T14:20:14Z |
| format | Article |
| id | doaj.art-78961029f15e41d7bb3e3fcbc40b7ba6 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-08T14:20:14Z |
| publishDate | 2024-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-78961029f15e41d7bb3e3fcbc40b7ba62024-01-14T12:06:55ZengSpringerOpenJournal of High Energy Physics1029-84792024-01-012024114810.1007/JHEP01(2024)031One- and two-dimensional higher-point conformal blocks as free-particle wavefunctions in AdS 3 ⊗ m $$ {\textrm{AdS}}_3^{\otimes m} $$Jean-François Fortin0Wen-Jie Ma1Sarthak Parikh2Lorenzo Quintavalle3Witold Skiba4Département de Physique, de Génie Physique et d’Optique, Université LavalBeijing Institute of Mathematical Sciences and Applications (BIMSA)Department of Physics, Indian Institute of Technology DelhiDépartement de Physique, de Génie Physique et d’Optique, Université LavalDepartment of Physics, Yale UniversityAbstract We establish that all of the one- and two-dimensional global conformal blocks are, up to some choice of prefactor, free-particle wavefunctions in tensor products of AdS3 or limits thereof. Our first core observation is that the six-point comb-channel conformal blocks correspond to free-particle wavefunctions on an AdS3 constructed directly in cross-ratio space. This construction generalizes to blocks for a special class of diagrams, which are determined as free-particle wavefunctions in tensor products of AdS3. Conformal blocks for all the remaining topologies are obtained as limits of the free wavefunctions mentioned above. Our results show directly that the integrable models associated with all one- and two-dimensional conformal blocks can be seen as limits of free theory, and manifest a relation between AdS and CFT kinematics that lies outside of the standard AdS/CFT dictionary. We complete the discussion by providing explicit Feynman-like rules that can be used to work out blocks for all topologies, as well as a Mathematica notebook that allows simple computation of Casimir equations and series expansions for blocks, by requiring just an OPE diagram as input.https://doi.org/10.1007/JHEP01(2024)031Scale and Conformal SymmetriesSpace-Time SymmetriesIntegrable HierarchiesGlobal Symmetries |
| spellingShingle | Jean-François Fortin Wen-Jie Ma Sarthak Parikh Lorenzo Quintavalle Witold Skiba One- and two-dimensional higher-point conformal blocks as free-particle wavefunctions in AdS 3 ⊗ m $$ {\textrm{AdS}}_3^{\otimes m} $$ Journal of High Energy Physics Scale and Conformal Symmetries Space-Time Symmetries Integrable Hierarchies Global Symmetries |
| title | One- and two-dimensional higher-point conformal blocks as free-particle wavefunctions in AdS 3 ⊗ m $$ {\textrm{AdS}}_3^{\otimes m} $$ |
| title_full | One- and two-dimensional higher-point conformal blocks as free-particle wavefunctions in AdS 3 ⊗ m $$ {\textrm{AdS}}_3^{\otimes m} $$ |
| title_fullStr | One- and two-dimensional higher-point conformal blocks as free-particle wavefunctions in AdS 3 ⊗ m $$ {\textrm{AdS}}_3^{\otimes m} $$ |
| title_full_unstemmed | One- and two-dimensional higher-point conformal blocks as free-particle wavefunctions in AdS 3 ⊗ m $$ {\textrm{AdS}}_3^{\otimes m} $$ |
| title_short | One- and two-dimensional higher-point conformal blocks as free-particle wavefunctions in AdS 3 ⊗ m $$ {\textrm{AdS}}_3^{\otimes m} $$ |
| title_sort | one and two dimensional higher point conformal blocks as free particle wavefunctions in ads 3 ⊗ m textrm ads 3 otimes m |
| topic | Scale and Conformal Symmetries Space-Time Symmetries Integrable Hierarchies Global Symmetries |
| url | https://doi.org/10.1007/JHEP01(2024)031 |
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