On local fields invariant under the action of topological defects
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918043996651520 |
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| author | Konechny, Anatoly Vergioglou, Vasileios |
| author_facet | Konechny, Anatoly Vergioglou, Vasileios |
| contents | In the context of rational conformal field theories (RCFT) we look into the problem of constructing and classifying pairs consisting of a local operator and a topological defect which commutes or anticommutes with it. We discuss the bulk and boundary versions of the problem. In the latter one considers a conformal boundary condition, a boundary operator on it and a junction with a topological defect. In the case of the charge conjugation modular invariant commuting configurations in each problem can be obtained when a certain restriction on the fusion rules in realised. We study the corresponding fusion rule problems in detail. While in the bulk case it reduces to realising the $a\times b = c$ fusion rule which was studied in arXiv:2012.14689 [hep-th], in the boundary it leads to a new type of problem. We obtain a full solution to this problem for the $\mathrm{SU(3)}$ WZW theory, thus constructing a class of commuting boundary operators and junctions in that theory, and suggest an approach to general WZW theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04316 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On local fields invariant under the action of topological defects Konechny, Anatoly Vergioglou, Vasileios High Energy Physics - Theory Mathematical Physics In the context of rational conformal field theories (RCFT) we look into the problem of constructing and classifying pairs consisting of a local operator and a topological defect which commutes or anticommutes with it. We discuss the bulk and boundary versions of the problem. In the latter one considers a conformal boundary condition, a boundary operator on it and a junction with a topological defect. In the case of the charge conjugation modular invariant commuting configurations in each problem can be obtained when a certain restriction on the fusion rules in realised. We study the corresponding fusion rule problems in detail. While in the bulk case it reduces to realising the $a\times b = c$ fusion rule which was studied in arXiv:2012.14689 [hep-th], in the boundary it leads to a new type of problem. We obtain a full solution to this problem for the $\mathrm{SU(3)}$ WZW theory, thus constructing a class of commuting boundary operators and junctions in that theory, and suggest an approach to general WZW theories. |
| title | On local fields invariant under the action of topological defects |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2505.04316 |