A profusion of $1/2$ BPS Wilson loops in $\mathcal{N}=4$ Chern-Simons-matter theories

Abstract

We initiate the study of $1/2$ BPS Wilson loops in $\mathcal{N}=4$ Chern-Simons-matter theories in three dimensions. We consider a circular or linear quiver with Chern-Simons levels $k$, $-k$ and $0$, and focus on loops preserving one of the two $SU(2)$ subgroups of the $R$-symmetry. In the cases with no vanishing Chern-Simons levels, we find a pair of Wilson loops for each pair of adjacent nodes on the quiver connected by a hypermultiplet (nodes connected by twisted hypermultiplets have Wilson loops preserving another set of supercharges). We expect this classical pairwise degeneracy to be lifted by quantum corrections. In the case with nodes with vanishing Chern-Simons terms connected by twisted hypermultiplets, we find that the usual $1/4$ BPS Wilson loops are automatically enlarged to $1/2$ BPS, as happens also in 3-dimensional Yang-Mills theory. When the nodes with vanishing Chern-Simons levels are connected by untwisted hypermultiplets, we do not find any Wilson loops coupling to those nodes which are classically invariant. Rather, we find several loops whose supersymmetry variation, while non zero, vanishes in any correlation function, so is weakly zero. We expect only one linear combination of those Wilson loops to remain BPS when quantum corrections are included. We analyze the M-theory duals of those Wilson loops and comment on their degeneracy. We also show that these Wilson loops are cohomologically equivalent to certain $1/4$ BPS Wilson loops whose expectation value can be evaluated by the appropriate localized matrix model.

40 pages

References in corpus (11)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• Exact half-BPS Type IIB interface solutions I: Local solution and supersymmetric Janus
• Wilson Loops in Superconformal Chern-Simons Theory and Fundamental Strings in Anti-de Sitter Supergravity Dual
• Supersymmetric Wilson Loops in N=6 Super Chern-Simons-matter theory
• N = 8 Superconformal Chern--Simons Theories
• 1/2-BPS Wilson Loops and Vortices in ABJM Model
• N=4 Chern-Simons theories and wrapped M-branes in their gravity duals
• Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
• Topological Chern-Simons Sigma Model
• Holographical Description of BPS Wilson Loops in Flavored ABJM Theory

Cited by in corpus (25)

• Supersymmetric Wilson loops in N=4 super Chern-Simons-matter theory
• Roadmap on Wilson loops in 3d Chern-Simons-matter theories
• Framing and localization in Chern-Simons theories with matter
• Instanton Effects in Rank Deformed Superconformal Chern-Simons Theories from Topological Strings
• BPS Wilson loops in $\mathcal{N}\ge 2$ superconformal Chern-Simons-matter theories
• The quantum 1/2 BPS Wilson loop in $\mathcal{N}=4$ Chern-Simons-matter theories
• String theory duals of Wilson loops from Higgsing
• New BPS Wilson loops in $\mathcal{N}\text{= 4}$ circular quiver Chern-Simons-matter theories
• Notes on hyperloops in N=4 Chern-Simons-matter theories
• Interpolating Wilson loops and enriched RG flows
• A matrix model for the latitude Wilson loop in ABJM theory
• BPS Wilson loops and quiver varieties
• 1/3 BPS loops and defect CFTs in ABJM theory
• Wilson loops and defect RG flows in ABJM
• Two-Point Functions in ABJM Matrix Model
• 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
• Exact results for Wilson loops in orbifold ABJM theory
• Supersymmetric Wilson loops in two dimensions and duality
• Loop Operators in Three-Dimensional $\mathcal{N}=2$ Fishnet Theories
• Abelian dualities and line defect indices for 3d gauge theories
• Bootstrap of the defect 1/2 BPS Wilson lines in N=4 Chern-Simons-matter theories
• Universal sectors in superconformal defects
• A network of hyperloops
• Wilson loops in 3d $\mathcal{N}=4$ SQCD from Fermi gas