Exact results for vortex loop operators in 3d supersymmetric theories

TY - JOUR

T1 - Exact results for vortex loop operators in 3d supersymmetric theories

AU - Drukker, Nadav

AU - Okuda, Takuya

AU - Passerini, Filippo

N1 - © 2014 The Author(s).

PY - 2014/7

Y1 - 2014/7

N2 - 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 x 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.

AB - 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 x 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.

KW - Supersymmetric gauge theory

KW - Wilson

KW - 't Hooft and Polyakov loops

KW - Duality in Gauge Field Theories

KW - 3-DIMENSIONAL GAUGE-THEORIES

KW - MIRROR SYMMETRY

U2 - 10.1007/JHEP07(2014)137

DO - 10.1007/JHEP07(2014)137

M3 - Article

SN - 1029-8479

VL - 2014

SP - 1

EP - 66

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 7

M1 - 137

ER -