Defect networks and supersymmetric loop operators

We consider topological defect networks with junctions in A(N) - 1 Toda CFT and the connection to supersymmetric loop operators in N = 2 theories of class S on a four- sphere. Correlation functions in the presence of topological defect networks are computed by exploiting the monodromy of conformal blocks, generalising the notion of a Verlinde operator. Concentrating on a class of topological defects in A(2) Toda theory, we find that the Verlinde operators generate an algebra whose structure is determined by a set of generalised skein relations that encode the representation theory of a quantum group. In the second half of the paper, we explore the dictionary between topological defect networks and supersymmetric loop operators in the N = 2* theory by comparing to exact localisation computations. In this context, the the generalised skein relations are related to the operator product expansion of loop operators.