Exploring replica-Potts CFTs in two dimensions
Abstract We initiate a numerical conformal bootstrap study of CFTs with S n ⋉ (S Q ) n global symmetry. These include CFTs that can be obtained as coupled replicas of two-dimensional critical Potts models. Particular attention is paid to the special case S 3 ⋉ (S 3)3, which governs the critical beh...
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SpringerOpen
2024-11-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP11(2024)030 |
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| author | Stefanos R. Kousvos Alessandro Piazza Alessandro Vichi |
| author_facet | Stefanos R. Kousvos Alessandro Piazza Alessandro Vichi |
| author_sort | Stefanos R. Kousvos |
| collection | DOAJ |
| description | Abstract We initiate a numerical conformal bootstrap study of CFTs with S n ⋉ (S Q ) n global symmetry. These include CFTs that can be obtained as coupled replicas of two-dimensional critical Potts models. Particular attention is paid to the special case S 3 ⋉ (S 3)3, which governs the critical behaviour of three coupled critical 3-state Potts models, a multi-scalar realisation of a (potentially) non-integrable CFT in two dimensions. The model has been studied in earlier works using perturbation theory, transfer matrices, and Monte Carlo simulations. This work represents an independent non-perturbative analysis. Our results are in agreement with previous determinations: we obtain an allowed peninsula within parameter space for the scaling dimensions of the three lowest-lying operators in the theory, which contains the earlier predictions for these scaling dimensions. Additionally, we derive numerous bounds on admissible scaling dimensions in the theory, which are compatible with earlier results. Our work sets the necessary groundwork for a future precision study of these theories in the conformal bootstrap. |
| format | Article |
| id | doaj-art-69c7e573375e4d5e9f6974ff7c61672d |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-69c7e573375e4d5e9f6974ff7c61672d2025-01-26T12:12:22ZengSpringerOpenJournal of High Energy Physics1029-84792024-11-0120241114610.1007/JHEP11(2024)030Exploring replica-Potts CFTs in two dimensionsStefanos R. Kousvos0Alessandro Piazza1Alessandro Vichi2Department of Physics, University of Pisa and INFN, section of PisaDepartment of Physics, University of Pisa and INFN, section of PisaDepartment of Physics, University of Pisa and INFN, section of PisaAbstract We initiate a numerical conformal bootstrap study of CFTs with S n ⋉ (S Q ) n global symmetry. These include CFTs that can be obtained as coupled replicas of two-dimensional critical Potts models. Particular attention is paid to the special case S 3 ⋉ (S 3)3, which governs the critical behaviour of three coupled critical 3-state Potts models, a multi-scalar realisation of a (potentially) non-integrable CFT in two dimensions. The model has been studied in earlier works using perturbation theory, transfer matrices, and Monte Carlo simulations. This work represents an independent non-perturbative analysis. Our results are in agreement with previous determinations: we obtain an allowed peninsula within parameter space for the scaling dimensions of the three lowest-lying operators in the theory, which contains the earlier predictions for these scaling dimensions. Additionally, we derive numerous bounds on admissible scaling dimensions in the theory, which are compatible with earlier results. Our work sets the necessary groundwork for a future precision study of these theories in the conformal bootstrap.https://doi.org/10.1007/JHEP11(2024)030Conformal and W SymmetryScale and Conformal SymmetriesRenormalization Group |
| spellingShingle | Stefanos R. Kousvos Alessandro Piazza Alessandro Vichi Exploring replica-Potts CFTs in two dimensions Journal of High Energy Physics Conformal and W Symmetry Scale and Conformal Symmetries Renormalization Group |
| title | Exploring replica-Potts CFTs in two dimensions |
| title_full | Exploring replica-Potts CFTs in two dimensions |
| title_fullStr | Exploring replica-Potts CFTs in two dimensions |
| title_full_unstemmed | Exploring replica-Potts CFTs in two dimensions |
| title_short | Exploring replica-Potts CFTs in two dimensions |
| title_sort | exploring replica potts cfts in two dimensions |
| topic | Conformal and W Symmetry Scale and Conformal Symmetries Renormalization Group |
| url | https://doi.org/10.1007/JHEP11(2024)030 |
| work_keys_str_mv | AT stefanosrkousvos exploringreplicapottscftsintwodimensions AT alessandropiazza exploringreplicapottscftsintwodimensions AT alessandrovichi exploringreplicapottscftsintwodimensions |