LEADER 03243nam 2200529 450 001 9910637706403321 005 20230507114349.0 010 $a3-031-14682-4 024 7 $a10.1007/978-3-031-14682-4 035 $a(MiAaPQ)EBC7167803 035 $a(Au-PeEL)EBL7167803 035 $a(CKB)25936408600041 035 $a(DE-He213)978-3-031-14682-4 035 $a(PPN)267809174 035 $a(EXLCZ)9925936408600041 100 $a20230507d2023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aString-net construction of RCFT correlators /$fJu?rgen Fuchs, Christoph Schweigert, and Yang Yang 205 $a1st ed. 2022. 210 1$aCham, Switzerland :$cSpringer,$d[2023] 210 4$d©2023 215 $a1 online resource (129 pages) 225 1 $aSpringerBriefs in Mathematical Physics,$x2197-1765 ;$v45 311 08$aPrint version: Fuchs, Jürgen String-Net Construction of RCFT Correlators Cham : Springer International Publishing AG,c2023 9783031146817 320 $aIncludes bibliographical references. 327 $aIntroduction -- Correlators in rational conformal field theory -- Correlators from string nets -- Correlators of particular interest -- Braided Eckmann-Hilton relation -- Universal correlators -- Appendix. 330 $aThis book studies using string-net models to accomplish a direct, purely two-dimensional, approach to correlators of two-dimensional rational conformal field theories. The authors obtain concise geometric expressions for the objects describing bulk and boundary fields in terms of idempotents in the cylinder category of the underlying modular fusion category, comprising more general classes of fields than is standard in the literature. Combining these idempotents with Frobenius graphs on the world sheet yields string nets that form a consistent system of correlators, i.e. a system of invariants under appropriate mapping class groups that are compatible with factorization. The authors extract operator products of field objects from specific correlators; the resulting operator products are natural algebraic expressions that make sense beyond semisimplicity. They also derive an Eckmann-Hilton relation internal to a braided category, thereby demonstrating the utility of string nets for understanding algebra in braided tensor categories. Finally, they introduce the notion of a universal correlator. This systematizes the treatment of situations in which different world sheets have the same correlator and allows for the definition of a more comprehensive mapping class group. 410 0$aSpringerBriefs in Mathematical Physics,$x2197-1765 ;$v45 606 $aQuantum field theory 606 $aParticles (Nuclear physics) 615 0$aQuantum field theory. 615 0$aParticles (Nuclear physics) 676 $a530.143 700 $aFuchs$b Ju?rgen$f1957 May 19-$0427703 702 $aSchweigert$b Christoph 702 $aYang$b Yang 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910637706403321 996 $aString-net construction of RCFT correlators$93363788 997 $aUNINA