Separation of variables in AdS/CFT: functional approach for the fishnet CFT
Abstract The major simplification in a number of quantum integrable systems is the existence of special coordinates in which the eigenstates take a factorised form. Despite many years of studies, the basis realising the separation of variables (SoV) remains unknown in N $$ \mathcal{N} $$ = 4 SYM and...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-06-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP06(2021)131 |
| _version_ | 1819063120244506624 |
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| author | Andrea Cavaglià Nikolay Gromov Fedor Levkovich-Maslyuk |
| author_facet | Andrea Cavaglià Nikolay Gromov Fedor Levkovich-Maslyuk |
| author_sort | Andrea Cavaglià |
| collection | DOAJ |
| description | Abstract The major simplification in a number of quantum integrable systems is the existence of special coordinates in which the eigenstates take a factorised form. Despite many years of studies, the basis realising the separation of variables (SoV) remains unknown in N $$ \mathcal{N} $$ = 4 SYM and similar models, even though it is widely believed they are integrable. In this paper we initiate the SoV approach for observables with nontrivial coupling dependence in a close cousin of N $$ \mathcal{N} $$ = 4 SYM — the fishnet 4D CFT. We develop the functional SoV formalism in this theory, which allows us to compute non-perturbatively some nontrivial observables in a form suitable for numerical evaluation. We present some applications of these methods. In particular, we discuss the possible SoV structure of the one-point correlators in presence of a defect, and write down a SoV-type expression for diagonal OPE coefficients involving an arbitrary state and the Lagrangian density operator. We believe that many of the findings of this paper can be applied in the N $$ \mathcal{N} $$ = 4 SYM case, as we speculate in the last part of the article. |
| first_indexed | 2024-12-21T15:09:37Z |
| format | Article |
| id | doaj.art-1e914426fedf48acb3a7d51101bad16b |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-21T15:09:37Z |
| publishDate | 2021-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-1e914426fedf48acb3a7d51101bad16b2022-12-21T18:59:19ZengSpringerOpenJournal of High Energy Physics1029-84792021-06-012021617410.1007/JHEP06(2021)131Separation of variables in AdS/CFT: functional approach for the fishnet CFTAndrea Cavaglià0Nikolay Gromov1Fedor Levkovich-Maslyuk2Mathematics Department, King’s College LondonMathematics Department, King’s College LondonInstitut de Physique Théorique, Université Paris Saclay, CEA, CNRSAbstract The major simplification in a number of quantum integrable systems is the existence of special coordinates in which the eigenstates take a factorised form. Despite many years of studies, the basis realising the separation of variables (SoV) remains unknown in N $$ \mathcal{N} $$ = 4 SYM and similar models, even though it is widely believed they are integrable. In this paper we initiate the SoV approach for observables with nontrivial coupling dependence in a close cousin of N $$ \mathcal{N} $$ = 4 SYM — the fishnet 4D CFT. We develop the functional SoV formalism in this theory, which allows us to compute non-perturbatively some nontrivial observables in a form suitable for numerical evaluation. We present some applications of these methods. In particular, we discuss the possible SoV structure of the one-point correlators in presence of a defect, and write down a SoV-type expression for diagonal OPE coefficients involving an arbitrary state and the Lagrangian density operator. We believe that many of the findings of this paper can be applied in the N $$ \mathcal{N} $$ = 4 SYM case, as we speculate in the last part of the article.https://doi.org/10.1007/JHEP06(2021)131Conformal Field TheoryIntegrable Field TheoriesLattice Integrable ModelsAdS-CFT Correspondence |
| spellingShingle | Andrea Cavaglià Nikolay Gromov Fedor Levkovich-Maslyuk Separation of variables in AdS/CFT: functional approach for the fishnet CFT Journal of High Energy Physics Conformal Field Theory Integrable Field Theories Lattice Integrable Models AdS-CFT Correspondence |
| title | Separation of variables in AdS/CFT: functional approach for the fishnet CFT |
| title_full | Separation of variables in AdS/CFT: functional approach for the fishnet CFT |
| title_fullStr | Separation of variables in AdS/CFT: functional approach for the fishnet CFT |
| title_full_unstemmed | Separation of variables in AdS/CFT: functional approach for the fishnet CFT |
| title_short | Separation of variables in AdS/CFT: functional approach for the fishnet CFT |
| title_sort | separation of variables in ads cft functional approach for the fishnet cft |
| topic | Conformal Field Theory Integrable Field Theories Lattice Integrable Models AdS-CFT Correspondence |
| url | https://doi.org/10.1007/JHEP06(2021)131 |
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