The Evaluation of Graphs on Surfaces for State-Sum Models with Defects
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866917839557885952 |
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| author | Farnsteiner, Julian Schweigert, Christoph |
| author_facet | Farnsteiner, Julian Schweigert, Christoph |
| contents | The evaluation of graphs on 2-spheres is a central ingredient of the Turaev-Viro construction of three-dimensional topological field theories. In this article, we introduce a class of graphs, called extruded graphs, that is relevant for the Turaev-Viro construction with general defect configurations involving defects of various dimensions. We define the evaluation of extruded graphs and show that it is invariant under a set of moves. This ensures the computability and uniqueness of our evaluation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_01946 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Evaluation of Graphs on Surfaces for State-Sum Models with Defects Farnsteiner, Julian Schweigert, Christoph Quantum Algebra Mathematical Physics Category Theory The evaluation of graphs on 2-spheres is a central ingredient of the Turaev-Viro construction of three-dimensional topological field theories. In this article, we introduce a class of graphs, called extruded graphs, that is relevant for the Turaev-Viro construction with general defect configurations involving defects of various dimensions. We define the evaluation of extruded graphs and show that it is invariant under a set of moves. This ensures the computability and uniqueness of our evaluation. |
| title | The Evaluation of Graphs on Surfaces for State-Sum Models with Defects |
| topic | Quantum Algebra Mathematical Physics Category Theory |
| url | https://arxiv.org/abs/2312.01946 |