Authors: Nadav Drukker Takuya Okuda Filippo Passerini
Publish Date: 2014/07/28
Volume: 2014, Issue: 7, Pages: 137-
Abstract
Three dimensional field theories admit disorder line operators dubbed vortex loop operators They are defined by the path integral in the presence of prescribed singularities along the defect line We study halfBPS vortex loop operators for mathcalN = 2 supersymmetric theories on mathbbS 3 its deformation mathbbS b3 and mathbbS 1 × mathbbS 2 We construct BPS vortex loops defined by the path integral with a fixed gauge or flavor holonomy for infinitesimal curves linking the loop It is also possible to include a singular profile for matter fields For vortex loops defined by holonomy we perform supersymmetric localization by calculating the fluctuation modes or alternatively by applying the index theory for transversally elliptic operators We clarify how the latter method works in situations without fixed points of relevant isometries Abelian mirror symmetry transforms Wilson and vortex loops in a specific way In particular an ordinary Wilson loop transforms into a vortex loop for a flavor symmetry Our localization results confirm the predictions of abelian mirror symmetryThis article is published under an open access license Please check the Copyright Information section for details of this license and what reuse is permitted If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and reuse information please contact the Rights and Permissions team
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