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Durham University

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Publication details for Mathew Bullimore

Bullimore, Mathew (2015). Defect networks and supersymmetric loop operators. Journal of High Energy Physics 2015(2): 066.

Author(s) from Durham


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.