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Defect networks and supersymmetric loop operators

Bullimore, Mathew

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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.


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

Journal Article Type Article
Acceptance Date Jan 13, 2015
Online Publication Date Feb 10, 2015
Publication Date Feb 10, 2015
Deposit Date Jun 7, 2018
Publicly Available Date Jun 8, 2018
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2015
Issue 2
Article Number 066


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Copyright 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.

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