03243nam 2200529 450 991063770640332120230507114349.03-031-14682-410.1007/978-3-031-14682-4(MiAaPQ)EBC7167803(Au-PeEL)EBL7167803(CKB)25936408600041(DE-He213)978-3-031-14682-4(PPN)267809174(EXLCZ)992593640860004120230507d2023 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierString-net construction of RCFT correlators /Jürgen Fuchs, Christoph Schweigert, and Yang Yang1st ed. 2022.Cham, Switzerland :Springer,[2023]©20231 online resource (129 pages)SpringerBriefs in Mathematical Physics,2197-1765 ;45Print version: Fuchs, Jürgen String-Net Construction of RCFT Correlators Cham : Springer International Publishing AG,c2023 9783031146817 Includes bibliographical references.Introduction -- Correlators in rational conformal field theory -- Correlators from string nets -- Correlators of particular interest -- Braided Eckmann-Hilton relation -- Universal correlators -- Appendix.This book studies using string-net models to accomplish a direct, purely two-dimensional, approach to correlators of two-dimensional rational conformal field theories. The authors obtain concise geometric expressions for the objects describing bulk and boundary fields in terms of idempotents in the cylinder category of the underlying modular fusion category, comprising more general classes of fields than is standard in the literature. Combining these idempotents with Frobenius graphs on the world sheet yields string nets that form a consistent system of correlators, i.e. a system of invariants under appropriate mapping class groups that are compatible with factorization. The authors extract operator products of field objects from specific correlators; the resulting operator products are natural algebraic expressions that make sense beyond semisimplicity. They also derive an Eckmann-Hilton relation internal to a braided category, thereby demonstrating the utility of string nets for understanding algebra in braided tensor categories. Finally, they introduce the notion of a universal correlator. This systematizes the treatment of situations in which different world sheets have the same correlator and allows for the definition of a more comprehensive mapping class group.SpringerBriefs in Mathematical Physics,2197-1765 ;45Quantum field theoryParticles (Nuclear physics)Quantum field theory.Particles (Nuclear physics)530.143Fuchs Jürgen1957 May 19-427703Schweigert ChristophYang YangMiAaPQMiAaPQMiAaPQBOOK9910637706403321String-net construction of RCFT correlators3363788UNINA