Non-semisimple CFT/TFT correspondence I: General setup
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915647789727744 |
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| author | Hofer, Aaron Runkel, Ingo |
| author_facet | Hofer, Aaron Runkel, Ingo |
| contents | We extend the TFT construction of CFT correlators of [arXiv:hep-th/0204148] to so-called finite logarithmic CFTs for which the algebraic input data is no longer semisimple but still finite. More specifically, starting from the data of a chiral CFT given in the form of a not necessarily semisimple modular tensor category C we use a three dimensional topological field theory with surface defects based on the surgery TFT of [arXiv:1912.02063] to construct a full CFT as a braided monoidal oplax natural transformation.
We make our construction explicit in the example of the transparent surface defect, resulting in the so-called Cardy case. In particular, we consider topological line defects and their action on bulk fields in these logarithmic CFTs, providing a source of examples for non-invertible and non-semisimple topological symmetries. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_21231 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-semisimple CFT/TFT correspondence I: General setup Hofer, Aaron Runkel, Ingo Quantum Algebra High Energy Physics - Theory Mathematical Physics We extend the TFT construction of CFT correlators of [arXiv:hep-th/0204148] to so-called finite logarithmic CFTs for which the algebraic input data is no longer semisimple but still finite. More specifically, starting from the data of a chiral CFT given in the form of a not necessarily semisimple modular tensor category C we use a three dimensional topological field theory with surface defects based on the surgery TFT of [arXiv:1912.02063] to construct a full CFT as a braided monoidal oplax natural transformation. We make our construction explicit in the example of the transparent surface defect, resulting in the so-called Cardy case. In particular, we consider topological line defects and their action on bulk fields in these logarithmic CFTs, providing a source of examples for non-invertible and non-semisimple topological symmetries. |
| title | Non-semisimple CFT/TFT correspondence I: General setup |
| topic | Quantum Algebra High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2511.21231 |