Boundary terms and three-point functions: an AdS/CFT puzzle resolved
Abstract N = 8 $$ \mathcal{N}=8 $$ superconformal field theories, such as the ABJM theory at Chern-Simons level k = 1 or 2, contain 35 scalar operators O I J $$ {\mathcal{O}}_{IJ} $$ with Δ = 1 in the 35 v representation of SO(8). The 3-point correlation function of these operators is non-vanishing,...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-06-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP06(2017)053 |
| _version_ | 1818119470164475904 |
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| author | Daniel Z. Freedman Krzysztof Pilch Silviu S. Pufu Nicholas P. Warner |
| author_facet | Daniel Z. Freedman Krzysztof Pilch Silviu S. Pufu Nicholas P. Warner |
| author_sort | Daniel Z. Freedman |
| collection | DOAJ |
| description | Abstract N = 8 $$ \mathcal{N}=8 $$ superconformal field theories, such as the ABJM theory at Chern-Simons level k = 1 or 2, contain 35 scalar operators O I J $$ {\mathcal{O}}_{IJ} $$ with Δ = 1 in the 35 v representation of SO(8). The 3-point correlation function of these operators is non-vanishing, and indeed can be calculated non-perturbatively in the field theory. But its AdS4 gravity dual, obtained from gauged N = 8 $$ \mathcal{N}=8 $$ supergravity, has no cubic A 3 couplings in its Lagrangian, where A IJ is the bulk dual of O I J $$ {\mathcal{O}}_{IJ} $$ . So conventional Witten diagrams cannot furnish the field theory result. We show that the extension of bulk supersymmetry to the AdS4 boundary requires the introduction of a finite A 3 counterterm that does provide a perfect match to the 3-point correlator. Boundary supersymmetry also requires infinite counterterms which agree with the method of holographic renormalization. The generating functional of correlation functions of the Δ = 1 operators is the Legendre transform of the on-shell action, and the supersymmetry properties of this functional play a significant role in our treatment. |
| first_indexed | 2024-12-11T05:10:42Z |
| format | Article |
| id | doaj.art-3926e192025a46cdb6cb85f5babab542 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-11T05:10:42Z |
| publishDate | 2017-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-3926e192025a46cdb6cb85f5babab5422022-12-22T01:19:56ZengSpringerOpenJournal of High Energy Physics1029-84792017-06-012017615710.1007/JHEP06(2017)053Boundary terms and three-point functions: an AdS/CFT puzzle resolvedDaniel Z. Freedman0Krzysztof Pilch1Silviu S. Pufu2Nicholas P. Warner3SITP and Department of Physics, Stanford UniversityDepartment of Physics and Astronomy, University of Southern CaliforniaJoseph Henry Laboratories, Princeton UniversityDepartment of Physics and Astronomy, University of Southern CaliforniaAbstract N = 8 $$ \mathcal{N}=8 $$ superconformal field theories, such as the ABJM theory at Chern-Simons level k = 1 or 2, contain 35 scalar operators O I J $$ {\mathcal{O}}_{IJ} $$ with Δ = 1 in the 35 v representation of SO(8). The 3-point correlation function of these operators is non-vanishing, and indeed can be calculated non-perturbatively in the field theory. But its AdS4 gravity dual, obtained from gauged N = 8 $$ \mathcal{N}=8 $$ supergravity, has no cubic A 3 couplings in its Lagrangian, where A IJ is the bulk dual of O I J $$ {\mathcal{O}}_{IJ} $$ . So conventional Witten diagrams cannot furnish the field theory result. We show that the extension of bulk supersymmetry to the AdS4 boundary requires the introduction of a finite A 3 counterterm that does provide a perfect match to the 3-point correlator. Boundary supersymmetry also requires infinite counterterms which agree with the method of holographic renormalization. The generating functional of correlation functions of the Δ = 1 operators is the Legendre transform of the on-shell action, and the supersymmetry properties of this functional play a significant role in our treatment.http://link.springer.com/article/10.1007/JHEP06(2017)053AdS-CFT CorrespondenceExtended SupersymmetrySupergravity Models |
| spellingShingle | Daniel Z. Freedman Krzysztof Pilch Silviu S. Pufu Nicholas P. Warner Boundary terms and three-point functions: an AdS/CFT puzzle resolved Journal of High Energy Physics AdS-CFT Correspondence Extended Supersymmetry Supergravity Models |
| title | Boundary terms and three-point functions: an AdS/CFT puzzle resolved |
| title_full | Boundary terms and three-point functions: an AdS/CFT puzzle resolved |
| title_fullStr | Boundary terms and three-point functions: an AdS/CFT puzzle resolved |
| title_full_unstemmed | Boundary terms and three-point functions: an AdS/CFT puzzle resolved |
| title_short | Boundary terms and three-point functions: an AdS/CFT puzzle resolved |
| title_sort | boundary terms and three point functions an ads cft puzzle resolved |
| topic | AdS-CFT Correspondence Extended Supersymmetry Supergravity Models |
| url | http://link.springer.com/article/10.1007/JHEP06(2017)053 |
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