The Virasoro-Shapiro amplitude in AdS5 × S5 and level splitting of 10d conformal symmetry
Abstract The genus zero contribution to the four-point correlator O p 1 O p 2 O p 3 O p 4 $$ \left\langle {\mathcal{O}}_{p_1}{\mathcal{O}}_{p_2}{\mathcal{O}}_{p_3}{\mathcal{O}}_{p_4}\right\rangle $$ of half-BPS single-particle operators O p $$ {\mathcal{O}}_p $$ in N $$ \mathcal{N} $$ = 4 super Yang...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-11-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP11(2021)109 |
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| author | F. Aprile J. M. Drummond H. Paul M. Santagata |
| author_facet | F. Aprile J. M. Drummond H. Paul M. Santagata |
| author_sort | F. Aprile |
| collection | DOAJ |
| description | Abstract The genus zero contribution to the four-point correlator O p 1 O p 2 O p 3 O p 4 $$ \left\langle {\mathcal{O}}_{p_1}{\mathcal{O}}_{p_2}{\mathcal{O}}_{p_3}{\mathcal{O}}_{p_4}\right\rangle $$ of half-BPS single-particle operators O p $$ {\mathcal{O}}_p $$ in N $$ \mathcal{N} $$ = 4 super Yang-Mills, at strong coupling, computes the Virasoro-Shapiro amplitude of closed superstrings in AdS 5 × S 5. Combining Mellin space techniques, the large p limit, and data about the spectrum of two-particle operators at tree level in supergravity, we design a bootstrap algorithm which heavily constrains its α′ expansion. We use crossing symmetry, polynomiality in the Mellin variables and the large p limit to stratify the Virasoro-Shapiro amplitude away from the ten-dimensional flat space limit. Then we analyse the spectrum of exchanged two-particle operators at fixed order in the α′ expansion. We impose that the ten-dimensional spin of the spectrum visible at that order is bounded above in the same way as in the flat space amplitude. This constraint determines the Virasoro-Shapiro amplitude in AdS 5 × S 5 up to a small number of ambiguities at each order. We compute it explicitly for (α′)5,6,7,8,9. As the order of α′ grows, the ten dimensional spin grows, and the set of visible two-particle operators opens up. Operators illuminated for the first time receive a string correction to their anomalous dimensions which is uniquely determined and lifts the residual degeneracy of tree level supergravity, due to ten-dimensional conformal symmetry. We encode the lifting of the residual degeneracy in a characteristic polynomial. This object carries information about all orders in α′. It is analytic in the quantum numbers, symmetric under an AdS 5 ↔ S 5 exchange, and it enjoys intriguing properties, which we explain and detail in various cases. |
| first_indexed | 2024-12-23T03:10:00Z |
| format | Article |
| id | doaj.art-d64d7282ecf94797b61226c834d43752 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-23T03:10:00Z |
| publishDate | 2021-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-d64d7282ecf94797b61226c834d437522022-12-21T18:02:16ZengSpringerOpenJournal of High Energy Physics1029-84792021-11-0120211116410.1007/JHEP11(2021)109The Virasoro-Shapiro amplitude in AdS5 × S5 and level splitting of 10d conformal symmetryF. Aprile0J. M. Drummond1H. Paul2M. Santagata3Dipartimento di Fisica, Università di Milano-Bicocca and INFN, Sezione di Milano-BicoccaSchool of Physics and Astronomy and STAG Research Centre, University of SouthamptonSchool of Physics and Astronomy and STAG Research Centre, University of SouthamptonSchool of Physics and Astronomy and STAG Research Centre, University of SouthamptonAbstract The genus zero contribution to the four-point correlator O p 1 O p 2 O p 3 O p 4 $$ \left\langle {\mathcal{O}}_{p_1}{\mathcal{O}}_{p_2}{\mathcal{O}}_{p_3}{\mathcal{O}}_{p_4}\right\rangle $$ of half-BPS single-particle operators O p $$ {\mathcal{O}}_p $$ in N $$ \mathcal{N} $$ = 4 super Yang-Mills, at strong coupling, computes the Virasoro-Shapiro amplitude of closed superstrings in AdS 5 × S 5. Combining Mellin space techniques, the large p limit, and data about the spectrum of two-particle operators at tree level in supergravity, we design a bootstrap algorithm which heavily constrains its α′ expansion. We use crossing symmetry, polynomiality in the Mellin variables and the large p limit to stratify the Virasoro-Shapiro amplitude away from the ten-dimensional flat space limit. Then we analyse the spectrum of exchanged two-particle operators at fixed order in the α′ expansion. We impose that the ten-dimensional spin of the spectrum visible at that order is bounded above in the same way as in the flat space amplitude. This constraint determines the Virasoro-Shapiro amplitude in AdS 5 × S 5 up to a small number of ambiguities at each order. We compute it explicitly for (α′)5,6,7,8,9. As the order of α′ grows, the ten dimensional spin grows, and the set of visible two-particle operators opens up. Operators illuminated for the first time receive a string correction to their anomalous dimensions which is uniquely determined and lifts the residual degeneracy of tree level supergravity, due to ten-dimensional conformal symmetry. We encode the lifting of the residual degeneracy in a characteristic polynomial. This object carries information about all orders in α′. It is analytic in the quantum numbers, symmetric under an AdS 5 ↔ S 5 exchange, and it enjoys intriguing properties, which we explain and detail in various cases.https://doi.org/10.1007/JHEP11(2021)1091/N ExpansionAdS-CFT CorrespondenceScattering Amplitudes |
| spellingShingle | F. Aprile J. M. Drummond H. Paul M. Santagata The Virasoro-Shapiro amplitude in AdS5 × S5 and level splitting of 10d conformal symmetry Journal of High Energy Physics 1/N Expansion AdS-CFT Correspondence Scattering Amplitudes |
| title | The Virasoro-Shapiro amplitude in AdS5 × S5 and level splitting of 10d conformal symmetry |
| title_full | The Virasoro-Shapiro amplitude in AdS5 × S5 and level splitting of 10d conformal symmetry |
| title_fullStr | The Virasoro-Shapiro amplitude in AdS5 × S5 and level splitting of 10d conformal symmetry |
| title_full_unstemmed | The Virasoro-Shapiro amplitude in AdS5 × S5 and level splitting of 10d conformal symmetry |
| title_short | The Virasoro-Shapiro amplitude in AdS5 × S5 and level splitting of 10d conformal symmetry |
| title_sort | virasoro shapiro amplitude in ads5 s5 and level splitting of 10d conformal symmetry |
| topic | 1/N Expansion AdS-CFT Correspondence Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP11(2021)109 |
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