Exact results for vortex loop operators in 3d supersymmetric theories

• Published in: The journal of high energy physics 2014-07, Vol.2014 (7), p.1, Article 137
• Main Authors: Drukker, Nadav, Okuda, Takuya, Passerini, Filippo
• Format: Article
• Language: English
• Subjects: Classical and Quantum Gravitation; Elementary Particles; High energy physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Relativity Theory; String Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP07(2014)137

A bstract 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 half-BPS vortex loop operators for N = 2 supersymmetric theories on S 3 , its deformation S b 3 and S 1 × S 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 symmetry.