Consistent systems of correlators in non-semisimple conformal field theory

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• 作者：Jü ; rgen Fuchs^a ; Christoph Schweigert^b ; ^{christoph.schweigert@uni-hamburg.de}
• 关键词：Non-semisimple conformal field theory ; Logarithmic conformal field theory ; Finite ribbon category ; Frobenius algebra ; Correlation function ; Modular functor
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：5 February 2017
• 年：2017
• 卷：307
• 期：Complete
• 页码：598-639
• 全文大小：887 K
• 卷排序：307

文摘

Based on the modular functor associated with a – not necessarily semisimple – finite non-degenerate ribbon category DD, we present a definition of a consistent system of bulk field correlators for a conformal field theory which comprises invariance under mapping class group actions and compatibility with the sewing of surfaces. We show that when restricting to surfaces of genus zero such systems are in bijection with commutative symmetric Frobenius algebras in DD, while for surfaces of any genus they are in bijection with modular Frobenius algebras in DD. This provides additional insight into structures familiar from rational conformal field theories and extends them to rigid logarithmic conformal field theories.