The 4-CB algebra and solvable lattice models
Abstract We study the algebras underlying solvable lattice models of the type fusion interaction round the face (IRF). We propose that the algebras are universal, depending only on the number of blocks, which is the degree of polynomial equation obeyed by the Boltzmann weights. Using the Yang-Baxter...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-11-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP11(2019)155 |
| _version_ | 1818190419084705792 |
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| author | Vladimir Belavin Doran Gepner Jian-Rong Li Ran Tessler |
| author_facet | Vladimir Belavin Doran Gepner Jian-Rong Li Ran Tessler |
| author_sort | Vladimir Belavin |
| collection | DOAJ |
| description | Abstract We study the algebras underlying solvable lattice models of the type fusion interaction round the face (IRF). We propose that the algebras are universal, depending only on the number of blocks, which is the degree of polynomial equation obeyed by the Boltzmann weights. Using the Yang-Baxter equation and the ansatz for the Baxterization of the models, we show that the three blocks models obey a version of Birman-MurakamiWenzl (BMW) algebra. For four blocks, we conjecture that the algebra, which is termed 4-CB (Conformal Braiding) algebra, is the BMW algebra with a different skein relation, along with one additional relation, and we provide evidence for this conjecture. We connect these algebras to knot theory by conjecturing new link invariants. The link invariants, in the case of four blocks, depend on three arbitrary parameters. We check our result for G 2 model with the seven dimensional representation and for SU(2) with the isospin 3/2 representation, which are both four blocks theories. |
| first_indexed | 2024-12-11T23:58:24Z |
| format | Article |
| id | doaj.art-3428c014aea24502a0949b54ff07b0fa |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-11T23:58:24Z |
| publishDate | 2019-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-3428c014aea24502a0949b54ff07b0fa2022-12-22T00:45:18ZengSpringerOpenJournal of High Energy Physics1029-84792019-11-0120191113610.1007/JHEP11(2019)155The 4-CB algebra and solvable lattice modelsVladimir Belavin0Doran Gepner1Jian-Rong Li2Ran Tessler3Physics Department, Ariel UniversityDepartment of Particle Physics and Astrophysics, Weizmann InstituteInstitute of Mathematics and Scientific Computing, University of GrazDepartment of Mathematics, Weizmann InstituteAbstract We study the algebras underlying solvable lattice models of the type fusion interaction round the face (IRF). We propose that the algebras are universal, depending only on the number of blocks, which is the degree of polynomial equation obeyed by the Boltzmann weights. Using the Yang-Baxter equation and the ansatz for the Baxterization of the models, we show that the three blocks models obey a version of Birman-MurakamiWenzl (BMW) algebra. For four blocks, we conjecture that the algebra, which is termed 4-CB (Conformal Braiding) algebra, is the BMW algebra with a different skein relation, along with one additional relation, and we provide evidence for this conjecture. We connect these algebras to knot theory by conjecturing new link invariants. The link invariants, in the case of four blocks, depend on three arbitrary parameters. We check our result for G 2 model with the seven dimensional representation and for SU(2) with the isospin 3/2 representation, which are both four blocks theories.http://link.springer.com/article/10.1007/JHEP11(2019)155Conformal Field TheoryLattice Integrable ModelsIntegrable Field Theories |
| spellingShingle | Vladimir Belavin Doran Gepner Jian-Rong Li Ran Tessler The 4-CB algebra and solvable lattice models Journal of High Energy Physics Conformal Field Theory Lattice Integrable Models Integrable Field Theories |
| title | The 4-CB algebra and solvable lattice models |
| title_full | The 4-CB algebra and solvable lattice models |
| title_fullStr | The 4-CB algebra and solvable lattice models |
| title_full_unstemmed | The 4-CB algebra and solvable lattice models |
| title_short | The 4-CB algebra and solvable lattice models |
| title_sort | 4 cb algebra and solvable lattice models |
| topic | Conformal Field Theory Lattice Integrable Models Integrable Field Theories |
| url | http://link.springer.com/article/10.1007/JHEP11(2019)155 |
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