BPS Wilson loops and quiver varieties

Abstract

Three dimensional supersymmetric field theories have large moduli spaces of circular Wilson loops preserving a fixed set of supercharges. We simplify previous constructions of such Wilson loops and amend and clarify their classification. For a generic quiver gauge theory we identify the moduli space as a quotient of $C^m$ for some $m$ by an appropriate symmetry group. These spaces are quiver varieties associated to a cover of the original quiver or a subquiver thereof. This moduli space is generically singular and at the singularities there are large degeneracies of operators which seem different, but whose expectation values and correlation functions with all other gauge invariant operators are identical. The formulation presented here, where the Wilson loops are on $S^3$ or squashed $S_b^3$ also allows to directly implement a localization procedure on these observables, which previously required an indirect cohomological equivalence argument.

20 pages, 8 figures, 1 appendix. V2: Minor changes, citations added, published version

References in corpus (7)

• Notes on SUSY Gauge Theories on Three-Sphere
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• Supersymmetric Wilson Loops in N=6 Super Chern-Simons-matter theory
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Cited by in corpus (15)

• Broken global symmetries and defect conformal manifolds
• Line Operators in Chern-Simons-Matter Theories and Bosonization in Three Dimensions
• Classifying Superconformal Defects in Diverse Dimensions Part I: Superconformal Lines
• Notes on hyperloops in N=4 Chern-Simons-matter theories
• Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II -Perturbative Analysis and All-loop Resummation
• Wilson-loop One-point Functions in ABJM Theory
• Localization and Duality for ABJM Latitude Wilson Loops
• Wilson loops and defect RG flows in ABJM
• Fermionic Bogomolnyi-Prasad-Sommerfield Wilson loops in four-dimensional $\mathcal{N}=2$ superconformal gauge theories
• Conformal and non-conformal hyperloop deformations of the 1/2 BPS circle
• Classifying BPS bosonic Wilson loops in 3d $\mathcal{N}=4$ Chern-Simons-matter theories
• On the abundance of supersymmetric strings in $Ad{S}_3\times S^3\times S^3\times S^1$ describing BPS line operators
• BPS Wilson loops in mass-deformed ABJM theory: Fermi gas expansions and new defect CFT data
• Abelian dualities and line defect indices for 3d gauge theories
• A network of hyperloops