Free field realization of the BMS Ising model
Abstract In this work, we study the inhomogeneous BMS free fermion theory, and show that it gives a free field realization of the BMS Ising model. We find that besides the BMS symmetry there exists an anisotropic scaling symmetry in BMS free fermion theory. As a result, the symmetry of the theory ge...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2023-08-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP08(2023)116 |
| _version_ | 1827781268048183296 |
|---|---|
| author | Zhe-fei Yu Bin Chen |
| author_facet | Zhe-fei Yu Bin Chen |
| author_sort | Zhe-fei Yu |
| collection | DOAJ |
| description | Abstract In this work, we study the inhomogeneous BMS free fermion theory, and show that it gives a free field realization of the BMS Ising model. We find that besides the BMS symmetry there exists an anisotropic scaling symmetry in BMS free fermion theory. As a result, the symmetry of the theory gets enhanced to an infinite dimensional symmetry generated by a new type of BMS-Kac-Moody algebra, different from the one found in the BMS free scalar model. Besides the different coupling of the u(1) Kac-Moody current to the BMS algebra, the Kac-Moody level is nonvanishing now such that the corresponding modules are further enlarged to BMS-Kac-Moody staggered modules. We show that there exists an underlying W (2, 2, 1) structure in the operator product expansion of the currents, and the BMS-Kac-Moody staggered modules can be viewed as highest-weight modules of this W-algebra. Moreover we obtain the BMS Ising model by a fermion-boson duality. This BMS Ising model is not a minimal model with respect to BMS3, since the minimal model construction based on BMS Kac determinant always leads to chiral Virasoro minimal models. Instead, the underlying algebra of the BMS Ising model is the W (2, 2, 1)-algebra, which can be understood as a quantum conformal BMS3 algebra. |
| first_indexed | 2024-03-11T15:16:26Z |
| format | Article |
| id | doaj.art-0accfa702e324185a43d9a17764995c9 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-11T15:16:26Z |
| publishDate | 2023-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-0accfa702e324185a43d9a17764995c92023-10-29T12:11:08ZengSpringerOpenJournal of High Energy Physics1029-84792023-08-012023814710.1007/JHEP08(2023)116Free field realization of the BMS Ising modelZhe-fei Yu0Bin Chen1Center for High Energy Physics, Peking UniversitySchool of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking UniversityAbstract In this work, we study the inhomogeneous BMS free fermion theory, and show that it gives a free field realization of the BMS Ising model. We find that besides the BMS symmetry there exists an anisotropic scaling symmetry in BMS free fermion theory. As a result, the symmetry of the theory gets enhanced to an infinite dimensional symmetry generated by a new type of BMS-Kac-Moody algebra, different from the one found in the BMS free scalar model. Besides the different coupling of the u(1) Kac-Moody current to the BMS algebra, the Kac-Moody level is nonvanishing now such that the corresponding modules are further enlarged to BMS-Kac-Moody staggered modules. We show that there exists an underlying W (2, 2, 1) structure in the operator product expansion of the currents, and the BMS-Kac-Moody staggered modules can be viewed as highest-weight modules of this W-algebra. Moreover we obtain the BMS Ising model by a fermion-boson duality. This BMS Ising model is not a minimal model with respect to BMS3, since the minimal model construction based on BMS Kac determinant always leads to chiral Virasoro minimal models. Instead, the underlying algebra of the BMS Ising model is the W (2, 2, 1)-algebra, which can be understood as a quantum conformal BMS3 algebra.https://doi.org/10.1007/JHEP08(2023)116Conformal and W SymmetryField Theories in Lower DimensionsScale and Conformal SymmetriesSpace-Time Symmetries |
| spellingShingle | Zhe-fei Yu Bin Chen Free field realization of the BMS Ising model Journal of High Energy Physics Conformal and W Symmetry Field Theories in Lower Dimensions Scale and Conformal Symmetries Space-Time Symmetries |
| title | Free field realization of the BMS Ising model |
| title_full | Free field realization of the BMS Ising model |
| title_fullStr | Free field realization of the BMS Ising model |
| title_full_unstemmed | Free field realization of the BMS Ising model |
| title_short | Free field realization of the BMS Ising model |
| title_sort | free field realization of the bms ising model |
| topic | Conformal and W Symmetry Field Theories in Lower Dimensions Scale and Conformal Symmetries Space-Time Symmetries |
| url | https://doi.org/10.1007/JHEP08(2023)116 |
| work_keys_str_mv | AT zhefeiyu freefieldrealizationofthebmsisingmodel AT binchen freefieldrealizationofthebmsisingmodel |