2013/12/17 by Bullimore, Mathew
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1312.5001
We consider topological defect networks with junctions in AN-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 A2 Toda theory, we find that the Verlinde operators generate an algebra whose structure is determined by a set of generalised skein relations. These relations 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^* star 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.