A handbook of holographic 4-point functions
Abstract We present a comprehensive discussion of tree-level holographic 4-point functions of scalar operators in momentum space. We show that each individual Witten diagram satisfies the conformal Ward identities on its own and is thus a valid conformal correlator. When the β = ∆ − d/2 are half-int...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-12-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP12(2022)039 |
| _version_ | 1797860079624519680 |
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| author | Adam Bzowski Paul McFadden Kostas Skenderis |
| author_facet | Adam Bzowski Paul McFadden Kostas Skenderis |
| author_sort | Adam Bzowski |
| collection | DOAJ |
| description | Abstract We present a comprehensive discussion of tree-level holographic 4-point functions of scalar operators in momentum space. We show that each individual Witten diagram satisfies the conformal Ward identities on its own and is thus a valid conformal correlator. When the β = ∆ − d/2 are half-integral, with ∆ the dimensions of the operators and d the spacetime dimension, the Witten diagrams can be evaluated in closed form and we present explicit formulae for the case d = 3 and ∆ = 2, 3. These correlators require renormalization, which we carry out explicitly, and lead to new conformal anomalies and beta functions. Correlators of operators of different dimension may be linked via weight-shifting operators, which allow new correlators to be generated from given ‘seed’ correlators. We present a new derivation of weight-shifting operators in momentum space and uncover several subtleties associated with their use: such operators map exchange diagrams to a linear combination of exchange and contact diagrams, and special care must be taken when renormalization is required. |
| first_indexed | 2024-04-09T21:39:59Z |
| format | Article |
| id | doaj.art-53767229aa5e4c44a4b8182b43d0aca3 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-09T21:39:59Z |
| publishDate | 2022-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-53767229aa5e4c44a4b8182b43d0aca32023-03-26T11:04:16ZengSpringerOpenJournal of High Energy Physics1029-84792022-12-01202212110010.1007/JHEP12(2022)039A handbook of holographic 4-point functionsAdam Bzowski0Paul McFadden1Kostas Skenderis2Faculty of Physics, University of WarsawSchool of Mathematics, Statistics & Physics, Newcastle UniversitySTAG Research Center & Mathematical Sciences, University of SouthamptonAbstract We present a comprehensive discussion of tree-level holographic 4-point functions of scalar operators in momentum space. We show that each individual Witten diagram satisfies the conformal Ward identities on its own and is thus a valid conformal correlator. When the β = ∆ − d/2 are half-integral, with ∆ the dimensions of the operators and d the spacetime dimension, the Witten diagrams can be evaluated in closed form and we present explicit formulae for the case d = 3 and ∆ = 2, 3. These correlators require renormalization, which we carry out explicitly, and lead to new conformal anomalies and beta functions. Correlators of operators of different dimension may be linked via weight-shifting operators, which allow new correlators to be generated from given ‘seed’ correlators. We present a new derivation of weight-shifting operators in momentum space and uncover several subtleties associated with their use: such operators map exchange diagrams to a linear combination of exchange and contact diagrams, and special care must be taken when renormalization is required.https://doi.org/10.1007/JHEP12(2022)039AdS-CFT CorrespondenceConformal and W SymmetryRenormalization and RegularizationScale and Conformal Symmetries |
| spellingShingle | Adam Bzowski Paul McFadden Kostas Skenderis A handbook of holographic 4-point functions Journal of High Energy Physics AdS-CFT Correspondence Conformal and W Symmetry Renormalization and Regularization Scale and Conformal Symmetries |
| title | A handbook of holographic 4-point functions |
| title_full | A handbook of holographic 4-point functions |
| title_fullStr | A handbook of holographic 4-point functions |
| title_full_unstemmed | A handbook of holographic 4-point functions |
| title_short | A handbook of holographic 4-point functions |
| title_sort | handbook of holographic 4 point functions |
| topic | AdS-CFT Correspondence Conformal and W Symmetry Renormalization and Regularization Scale and Conformal Symmetries |
| url | https://doi.org/10.1007/JHEP12(2022)039 |
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