Defect networks and supersymmetric loop operators

Bullimore, Mathew

Abstract

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.

Citation

Bullimore, M. (2015). Defect networks and supersymmetric loop operators. Journal of High Energy Physics, 2015(2), Article 066. https://doi.org/10.1007/jhep02%282015%29066

• 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
• DOI: https://doi.org/10.1007/jhep02%282015%29066