On fusing matrices associated with conformal boundary conditions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914867352436736 |
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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 at the fusing matrices that arise when a topological defect is attached to a conformal boundary condition. We call such junctions open topological defects. One type of fusing matrices arises when two open defects fuse while another arises when an open defect passes through a boundary operator. We use the topological field theory approach to RCFTs based on Frobenius algebra objects in modular tensor categories to describe the general structure associated with such matrices and how to compute them from a given Frobenius algebra object and its representation theory. We illustrate the computational process on the rational free boson theories. Applications to boundary renormalisation group flows are briefly discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10189 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On fusing matrices associated with conformal boundary conditions Konechny, Anatoly Vergioglou, Vasileios High Energy Physics - Theory Mathematical Physics Category Theory In the context of rational conformal field theories (RCFT) we look at the fusing matrices that arise when a topological defect is attached to a conformal boundary condition. We call such junctions open topological defects. One type of fusing matrices arises when two open defects fuse while another arises when an open defect passes through a boundary operator. We use the topological field theory approach to RCFTs based on Frobenius algebra objects in modular tensor categories to describe the general structure associated with such matrices and how to compute them from a given Frobenius algebra object and its representation theory. We illustrate the computational process on the rational free boson theories. Applications to boundary renormalisation group flows are briefly discussed. |
| title | On fusing matrices associated with conformal boundary conditions |
| topic | High Energy Physics - Theory Mathematical Physics Category Theory |
| url | https://arxiv.org/abs/2405.10189 |