Abstract
We investigate several aspects of BPS latitude Wilson loops in gauge theories in three dimensions with mathcal{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.
Highlights
Extended operators or defects, those supported on sub-manifolds of positive dimension, play a central role in the study of gauge theory
We describe a class of Wilson loops in U(N1)k × U(N2)−k ABJM theory that preserve a certain fraction of the original N = 6 supersymmetry
We have examined several aspects of latitude Wilson loops in the ABJM model: a family of BPS loop operators parameterized by a real number ν
Summary
Those supported on sub-manifolds of positive dimension, play a central role in the study of gauge theory. We find an interesting relationship between the superalgebra preserved by latitude loops, in an appropriate limit, and that which governs Higgs and Coulomb branch operators, and the associated topological quantum mechanics, of standard N ≥ 4 theories These local operators were introduced in [21] and subsequently studied in [22,23,24]. We show that the matrix model obtained from considering this operator, ostensibly quite different, computes the same expectation value as the one which we derive for the latitude loop in ABJM. We identify the loop operator dual to the ABJM latitude and use supersymmetric localization to derive a matrix model for its expectation value.
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