TY - GEN digital ID - 131907098 TI - String-Net Construction of RCFT Correlators AU - Fuchs, Jürgen AU - Schweigert, Christoph AU - Yang, Yang PY - 2022 SN - 9783031146824 9783031146817 9783031146831 PB - Cham Springer International Publishing DB - UniCat KW - Ordered algebraic structures KW - Topological groups. Lie groups KW - Mathematical physics KW - Quantum mechanics. Quantumfield theory KW - Elementary particles KW - elementaire deeltjes KW - kwantumleer KW - wiskunde KW - fysica KW - topologie UR - https://www.unicat.be/uniCat?func=search&query=sysid:131907098 AB - 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. ER -