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arXiv · 2511.21231

Non-semisimple CFT/TFT correspondence I: General setup

Aaron Hofer·Ingo Runkel
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Abstract

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.

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Aaron Hofer, Ingo Runkel. 2025-12-02. Non-semisimple CFT/TFT correspondence I: General setup. https://arxiv.org/abs/2511.21231

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