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• W3100945542 abstract "This article develops new techniques for understanding the relationship between the three different mathematical formulations of two-dimensional chiral conformal field theory: conformal nets (axiomatizing local observables), vertex operator algebras (axiomatizing fields), and Segal CFTs. It builds upon previous work (Tener in Adv Math 349:488–563, 2019), which introduced a geometric interpolation procedure for constructing conformal nets from VOAs via Segal CFT, simultaneously relating all three frameworks. In this article, we extend this construction to study the relationship between the representation theory of conformal nets and the representation theory of vertex operator algebras. We define a correspondence between representations in the two contexts, and show how to construct representations of conformal nets from VOAs. We also show that this correspondence is rich enough to relate the respective ‘fusion product’ theories for conformal nets and VOAs, by constructing local intertwiners (in the sense of conformal nets) from intertwining operators (in the sense of VOAs). We use these techniques to show that all WZW conformal nets can be constructed using our geometric interpolation procedure." @default.
• W3100945542 created "2020-11-23" @default.
• W3100945542 creator A5037615806 @default.
• W3100945542 date "2019-11-25" @default.
• W3100945542 modified "2023-10-18" @default.
• W3100945542 title "Representation theory in chiral conformal field theory: from fields to observables" @default.
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• W3100945542 doi "https://doi.org/10.1007/s00029-019-0526-3" @default.
• W3100945542 hasPublicationYear "2019" @default.
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