Bethe states and Knizhnik-Zamolodchikov equations of the trigonometric Gaudin model with triangular boundary
We present a comprehensive treatment of the non-periodic trigonometric sℓ(2) Gaudin model with triangular boundary, with an emphasis on specific freedom found in the local realization of the generators, as well as in the creation operators used in the algebraic Bethe ansatz. First, we give Bethe vec...
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| Format: | Article |
| Language: | English |
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Elsevier
2021-08-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321321001590 |
| _version_ | 1818658249994403840 |
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| author | I. Salom N. Manojlović |
| author_facet | I. Salom N. Manojlović |
| author_sort | I. Salom |
| collection | DOAJ |
| description | We present a comprehensive treatment of the non-periodic trigonometric sℓ(2) Gaudin model with triangular boundary, with an emphasis on specific freedom found in the local realization of the generators, as well as in the creation operators used in the algebraic Bethe ansatz. First, we give Bethe vectors of the non-periodic trigonometric sℓ(2) Gaudin model both through a recurrence relation and in a closed form. Next, the off-shell action of the generating function of the trigonometric Gaudin Hamiltonians with general boundary terms on an arbitrary Bethe vector is shown, together with the corresponding proof based on mathematical induction. The action of the Gaudin Hamiltonians is given explicitly. Furthermore, by careful choice of the arbitrary functions appearing in our more general formulation, we additionally obtain: i) the solutions to the Knizhnik-Zamolodchikov equations (each corresponding to one of the Bethe states); ii) compact formulas for the on-shell norms of Bethe states; and iii) closed-form expressions for the off-shell scalar products of Bethe states. |
| first_indexed | 2024-12-17T03:54:23Z |
| format | Article |
| id | doaj.art-a45ad7caf9c54f789881fbeb66c49e41 |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-12-17T03:54:23Z |
| publishDate | 2021-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-a45ad7caf9c54f789881fbeb66c49e412022-12-21T22:04:40ZengElsevierNuclear Physics B0550-32132021-08-01969115462Bethe states and Knizhnik-Zamolodchikov equations of the trigonometric Gaudin model with triangular boundaryI. Salom0N. Manojlović1Institute of Physics, University of Belgrade, P.O. Box 57, 11080 Belgrade, Serbia; Corresponding author.Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade do Algarve, Campus de Gambelas, PT-8005-139 Faro, Portugal; Grupo de Física Matemática da Universidade de Lisboa, Departamento de Matemática, Faculdade de Ciências, Campo Grande, Edifício C6, PT-1749-016 Lisboa, PortugalWe present a comprehensive treatment of the non-periodic trigonometric sℓ(2) Gaudin model with triangular boundary, with an emphasis on specific freedom found in the local realization of the generators, as well as in the creation operators used in the algebraic Bethe ansatz. First, we give Bethe vectors of the non-periodic trigonometric sℓ(2) Gaudin model both through a recurrence relation and in a closed form. Next, the off-shell action of the generating function of the trigonometric Gaudin Hamiltonians with general boundary terms on an arbitrary Bethe vector is shown, together with the corresponding proof based on mathematical induction. The action of the Gaudin Hamiltonians is given explicitly. Furthermore, by careful choice of the arbitrary functions appearing in our more general formulation, we additionally obtain: i) the solutions to the Knizhnik-Zamolodchikov equations (each corresponding to one of the Bethe states); ii) compact formulas for the on-shell norms of Bethe states; and iii) closed-form expressions for the off-shell scalar products of Bethe states.http://www.sciencedirect.com/science/article/pii/S0550321321001590 |
| spellingShingle | I. Salom N. Manojlović Bethe states and Knizhnik-Zamolodchikov equations of the trigonometric Gaudin model with triangular boundary Nuclear Physics B |
| title | Bethe states and Knizhnik-Zamolodchikov equations of the trigonometric Gaudin model with triangular boundary |
| title_full | Bethe states and Knizhnik-Zamolodchikov equations of the trigonometric Gaudin model with triangular boundary |
| title_fullStr | Bethe states and Knizhnik-Zamolodchikov equations of the trigonometric Gaudin model with triangular boundary |
| title_full_unstemmed | Bethe states and Knizhnik-Zamolodchikov equations of the trigonometric Gaudin model with triangular boundary |
| title_short | Bethe states and Knizhnik-Zamolodchikov equations of the trigonometric Gaudin model with triangular boundary |
| title_sort | bethe states and knizhnik zamolodchikov equations of the trigonometric gaudin model with triangular boundary |
| url | http://www.sciencedirect.com/science/article/pii/S0550321321001590 |
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