BPS Wilson loops in $\mathcal{N}\ge 2$ superconformal Chern-Simons-matter theories

Abstract

In $\mathcal{N}\ge 2$ superconformal Chern-Simons-matter theories we construct the infinite family of Bogomol'nyi-Prasad-Sommerfield (BPS) Wilson loops featured by constant parametric couplings to scalar and fermion matter, including both line Wilson loops in Minkowski spacetime and circle Wilson loops in Euclidean space. We find that the connection of the most general BPS Wilson loop cannot be decomposed in terms of double-node connections. Moreover, if the quiver contains triangles, it cannot be interpreted as a supermatrix inside a superalgebra. However, for particular choices of the parameters it reduces to the well-known connections of 1/6 BPS Wilson loops in Aharony-Bergman-Jafferis-Maldacena (ABJM) theory and 1/4 BPS Wilson loops in $\mathcal{N}=4$ orbifold ABJM theory. In the particular case of $\mathcal{N}=2$ orbifold ABJM theory we identify the gravity duals of a subset of operators. We investigate the cohomological equivalence of fermionic and bosonic BPS Wilson loops at quantum level by studying their expectation values, and find strong evidence that the cohomological equivalence holds quantum mechanically, at framing one. Finally, we discuss a stronger formulation of the cohomological equivalence, which implies non-trivial identities for correlation functions of composite operators in the defect CFT defined on the Wilson contour and allows to make novel predictions on the corresponding unknown integrals that call for a confirmation.

arXiv comment53 pages, 12 figures

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• Roadmap on Wilson loops in 3d Chern-Simons-matter theories
• Marginal deformations and defect anomalies
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• Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II -Perturbative Analysis and All-loop Resummation
• The Quantum Theory of Chern-Simons Supergravity
• 1/3 BPS loops and defect CFTs in ABJM theory
• Fermionic Bogomolnyi-Prasad-Sommerfield Wilson loops in four-dimensional $\mathcal{N}=2$ superconformal gauge theories
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• 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
• Loop Operators in Three-Dimensional $\mathcal{N}=2$ Fishnet Theories
• Supersymmetric Wilson loops in two dimensions and duality
• 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
• Holographic Wilson Loop One-point Functions in ABJM Theory
• A network of hyperloops