Localization and duality for ABJM latitude Wilson loops

Abstract

We investigate several aspects of BPS latitude Wilson loops in gauge theories in three dimensions with $$ \mathcal{N} $$ N ≥ 4 supersymmetry. We derive a matrix model for the bosonic latitude Wilson loop in ABJM using supersymmetric localization, and show how to extend the computation to more general Chern-Simons-matter theories. We then define latitude type Wilson and vortex loop operators in theories without Chern-Simons terms, and explore a connection to the recently derived superalgebra defining local Higgs and Coulomb branch operators in these theories. Finally, we identify a BPS loop operator dual to the bosonic latitude Wilson loop which is a novel bound state of Wilson and vortex loops, defined using a worldvolume supersymmetric quantum mechanics.

Superconformal Line Defects in 3D

“…Very recently, the hard task of proving that the matrix model is the result of applying a localization procedure driven by a ν-dependent supercharge was taken on [81]. Though the authors did not manage to solve directly the very difficult problem of bringing the latitude supercharges off-shell as required to make localization work, they managed to show that matrix model ( 48) emerges as the result of applying the Källén approach [82] (generalized to Chern-Simons theories with matter in [83]) under the assumption that also for the latitude supersymmetry algebra, there exists a kind of topologically twisted Lagrangian as the one considered there, which is on-shell equivalent to the ABJM one.…”

Wilson loop correlators in $$ \mathcal{N} $$ = 2 superconformal quivers

“…Supersymmetric localization allows also to compute more general correlation functions that include local operators [5][6][7][8][9][10][11][12][13], the Bremsstrahlung function [14,15] or multiple insertions of Wilson loops and Wilson loops in higher dimensional representations [16][17][18][19][20]. Interesting attempts to extend these exact results to different frameworks have been achieved in two dimensions [21] and in the threedimensional analogue of N = 4, ABJM theory, where localization was still successfully implemented [22][23][24][25][26] and several observables have been computed exactly [27][28][29][30], see [31] for a recent review.…”

Superconformal line defects in 3D

“…Very recently the hard task of proving that the Matrix Model is the result of applying a localization procedure driven by a ν-dependent supercharge has been taken on [81]. Though the authors did not manage to solve directly the very difficult problem of bringing the latitude supercharges off-shell as required to make localization work, they managed to show that Matrix Model (4.18) emerges as the result of applying the Källén approach [82] (generalized to Chern-Simons theories with matter in [83]) under the assumption that also for the latitude supersymmetry algebra there exists kind of topologically twisted Lagrangian as the one considered there, which is on-shell equivalent to the ABJM one.…”