Bullimore, Mathew (2015) 'Defect networks and supersymmetric loop operators.', Journal of high energy physics., 2015 (2). 066.
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.
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|Publisher Web site:||https://doi.org/10.1007/JHEP02(2015)066|
|Publisher statement:||© The Author(s) 2015 Open Access This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.|
|Date accepted:||13 January 2015|
|Date deposited:||08 June 2018|
|Date of first online publication:||10 February 2015|
|Date first made open access:||No date available|
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