Three-point functions in ABJM and Bethe Ansatz
Abstract We develop an integrability-based framework to compute structure constants of two sub-determinant operators and a single-trace non-BPS operator in ABJM theory in the planar limit. In this first paper, we study them at weak coupling using a relation to an integrable spin chain. We first deve...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2022)002 |
| _version_ | 1819228666173849600 |
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| author | Peihe Yang Yunfeng Jiang Shota Komatsu Jun-Bao Wu |
| author_facet | Peihe Yang Yunfeng Jiang Shota Komatsu Jun-Bao Wu |
| author_sort | Peihe Yang |
| collection | DOAJ |
| description | Abstract We develop an integrability-based framework to compute structure constants of two sub-determinant operators and a single-trace non-BPS operator in ABJM theory in the planar limit. In this first paper, we study them at weak coupling using a relation to an integrable spin chain. We first develop a nested Bethe ansatz for an alternating SU(4) spin chain that describes single-trace operators made out of scalar fields. We then apply it to the computation of the structure constants and show that they are given by overlaps between a Bethe eigenstate and a matrix product state. We conjecture that the determinant operator corresponds to an integrable matrix product state and present a closed-form expression for the overlap, which resembles the so-called Gaudin determinant. We also provide evidence for the integrability of general sub-determinant operators. The techniques developed in this paper can be applied to other quantities in ABJM theory including three-point functions of single-trace operators. |
| first_indexed | 2024-12-23T11:00:54Z |
| format | Article |
| id | doaj.art-8bd244be6d294b8cafe42896635ed153 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-23T11:00:54Z |
| publishDate | 2022-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-8bd244be6d294b8cafe42896635ed1532022-12-21T17:49:39ZengSpringerOpenJournal of High Energy Physics1029-84792022-01-012022115010.1007/JHEP01(2022)002Three-point functions in ABJM and Bethe AnsatzPeihe Yang0Yunfeng Jiang1Shota Komatsu2Jun-Bao Wu3Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin UniversitySchool of physics, Southeast UniversityDepartment of Theoretical Physics, CERNCenter for Joint Quantum Studies and Department of Physics, School of Science, Tianjin UniversityAbstract We develop an integrability-based framework to compute structure constants of two sub-determinant operators and a single-trace non-BPS operator in ABJM theory in the planar limit. In this first paper, we study them at weak coupling using a relation to an integrable spin chain. We first develop a nested Bethe ansatz for an alternating SU(4) spin chain that describes single-trace operators made out of scalar fields. We then apply it to the computation of the structure constants and show that they are given by overlaps between a Bethe eigenstate and a matrix product state. We conjecture that the determinant operator corresponds to an integrable matrix product state and present a closed-form expression for the overlap, which resembles the so-called Gaudin determinant. We also provide evidence for the integrability of general sub-determinant operators. The techniques developed in this paper can be applied to other quantities in ABJM theory including three-point functions of single-trace operators.https://doi.org/10.1007/JHEP01(2022)0021/N ExpansionAdS-CFT CorrespondenceBethe AnsatzIntegrable Field Theories |
| spellingShingle | Peihe Yang Yunfeng Jiang Shota Komatsu Jun-Bao Wu Three-point functions in ABJM and Bethe Ansatz Journal of High Energy Physics 1/N Expansion AdS-CFT Correspondence Bethe Ansatz Integrable Field Theories |
| title | Three-point functions in ABJM and Bethe Ansatz |
| title_full | Three-point functions in ABJM and Bethe Ansatz |
| title_fullStr | Three-point functions in ABJM and Bethe Ansatz |
| title_full_unstemmed | Three-point functions in ABJM and Bethe Ansatz |
| title_short | Three-point functions in ABJM and Bethe Ansatz |
| title_sort | three point functions in abjm and bethe ansatz |
| topic | 1/N Expansion AdS-CFT Correspondence Bethe Ansatz Integrable Field Theories |
| url | https://doi.org/10.1007/JHEP01(2022)002 |
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