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.
