Computing four-point functions with integrability, bootstrap and parity symmetry
Abstract The combination of integrability and crossing symmetry has proven to give tight non-perturbative bounds on some planar structure constants in N $$ \mathcal{N} $$ =4 SYM, particularly in the setup of defect observables built on a Wilson-Maldacena line. Whereas the precision is good for the l...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-02-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP02(2025)026 |
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| author | Andrea Cavaglià Nikolay Gromov Michelangelo Preti |
| author_facet | Andrea Cavaglià Nikolay Gromov Michelangelo Preti |
| author_sort | Andrea Cavaglià |
| collection | DOAJ |
| description | Abstract The combination of integrability and crossing symmetry has proven to give tight non-perturbative bounds on some planar structure constants in N $$ \mathcal{N} $$ =4 SYM, particularly in the setup of defect observables built on a Wilson-Maldacena line. Whereas the precision is good for the low lying states, higher in the spectrum it drops due to the degeneracies at weak coupling when considering a single correlator. As this could be a clear obstacle in restoring higher point functions, we studied the problem of bounding directly a 4-point function at generic cross ratio, showing how to adapt for this purpose the numerical bootstrap algorithms based on semidefinite programming. Another tool we are using to further narrow the bounds is a parity symmetry descending from the N $$ \mathcal{N} $$ =4 SYM theory, which allowed us to reduce the number of parameters. We also give an interpretation for the parity in terms of the Quantum Spectral Curve at weak coupling. Our numerical bounds give an accurate determination of the 4-point function for physical values of the cross ratio, with at worst 5-6 digits precision at weak coupling and reaching more than 11 digits for ’t Hooft coupling λ 4 π ∼ 4 $$ \frac{\sqrt{\lambda }}{4\pi}\sim 4 $$ . |
| format | Article |
| id | doaj-art-7dd0bc30582e4ca59782af2983a3619b |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | SpringerOpen |
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| series | Journal of High Energy Physics |
| spelling | doaj-art-7dd0bc30582e4ca59782af2983a3619b2025-02-09T12:08:55ZengSpringerOpenJournal of High Energy Physics1029-84792025-02-012025213910.1007/JHEP02(2025)026Computing four-point functions with integrability, bootstrap and parity symmetryAndrea Cavaglià0Nikolay Gromov1Michelangelo Preti2Dipartimento di Fisica, Università di TorinoDepartment of Mathematics, King’s College LondonDipartimento di Fisica, Università di TorinoAbstract The combination of integrability and crossing symmetry has proven to give tight non-perturbative bounds on some planar structure constants in N $$ \mathcal{N} $$ =4 SYM, particularly in the setup of defect observables built on a Wilson-Maldacena line. Whereas the precision is good for the low lying states, higher in the spectrum it drops due to the degeneracies at weak coupling when considering a single correlator. As this could be a clear obstacle in restoring higher point functions, we studied the problem of bounding directly a 4-point function at generic cross ratio, showing how to adapt for this purpose the numerical bootstrap algorithms based on semidefinite programming. Another tool we are using to further narrow the bounds is a parity symmetry descending from the N $$ \mathcal{N} $$ =4 SYM theory, which allowed us to reduce the number of parameters. We also give an interpretation for the parity in terms of the Quantum Spectral Curve at weak coupling. Our numerical bounds give an accurate determination of the 4-point function for physical values of the cross ratio, with at worst 5-6 digits precision at weak coupling and reaching more than 11 digits for ’t Hooft coupling λ 4 π ∼ 4 $$ \frac{\sqrt{\lambda }}{4\pi}\sim 4 $$ .https://doi.org/10.1007/JHEP02(2025)026Extended SupersymmetryIntegrable Field TheoriesScale and Conformal SymmetriesWilson, ’t Hooft and Polyakov loops |
| spellingShingle | Andrea Cavaglià Nikolay Gromov Michelangelo Preti Computing four-point functions with integrability, bootstrap and parity symmetry Journal of High Energy Physics Extended Supersymmetry Integrable Field Theories Scale and Conformal Symmetries Wilson, ’t Hooft and Polyakov loops |
| title | Computing four-point functions with integrability, bootstrap and parity symmetry |
| title_full | Computing four-point functions with integrability, bootstrap and parity symmetry |
| title_fullStr | Computing four-point functions with integrability, bootstrap and parity symmetry |
| title_full_unstemmed | Computing four-point functions with integrability, bootstrap and parity symmetry |
| title_short | Computing four-point functions with integrability, bootstrap and parity symmetry |
| title_sort | computing four point functions with integrability bootstrap and parity symmetry |
| topic | Extended Supersymmetry Integrable Field Theories Scale and Conformal Symmetries Wilson, ’t Hooft and Polyakov loops |
| url | https://doi.org/10.1007/JHEP02(2025)026 |
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