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Consistent systems of correlators in non-semisimple conformal field theory. (English) Zbl 1355.81034

This paper presents a precise mathematical definition of the notions of bulk object and system of correlators of bulk fields (CBFs) for a conformal field theory corresponding to a given finite ribbon category \(\mathcal{D}\), as well as that of consistency of CBFs. The main novelty of this approach is that it does not require semi simplicity of \(\mathcal{D}\). The main results presented by the authors show: first, when constrained to genus zero surfaces a bijection between consistent CBFs and the structures of commutative symmetric Frobenius algebras; second if \(\mathcal{D}\) is in addition modular, then this bijection is with the structures of modular Frobenius algebras. These results are applicable not only to already known structures from rational conformal field theories but also to non-rational ones.

MSC:

81P40 Quantum coherence, entanglement, quantum correlations
57R56 Topological quantum field theories (aspects of differential topology)
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