BPS Wilson loops in Minkowski spacetime and Euclidean space

Abstract

We give evidence that spacelike BPS Wilson loops do not exist in Minkowski spacetime. We show that spacelike Wilson loops in Minkowski spacetime cannot preserve any supersymmetries, in $d=4$ $\mathcal{N}=4$ super Yang-Mills theory, $d=3$ $\mathcal{N}=2$ super Chern-Simons-matter theory, and $d=3$ $\mathcal{N}=6$ Aharony-Bergman-Jafferis-Maldacena theory. We not only show this using infinite straight lines and circles as examples, but also we give proofs for general curves. We attribute this to the conflicts of reality conditions of the spinors. However, spacelike Wilson loops do exist in Euclidean space. There are both BPS Wilson loops along infinite straight lines and circular BPS Wilson loops. This is because the reality conditions of the spinors are lost after Wick rotation. The result is reasonable in view of the AdS/CFT correspondence.

V1, 19 pages, no figure; V2, 25 pages, typos corrected and proofs for general curves added thanks to the careful reading and valuable suggestions of the anonymous referee, version to appear in EPJC; V3, 25 pages, published version

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Cited by in corpus (9)

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• String theory duals of Wilson loops from Higgsing
• New BPS Wilson loops in $\mathcal{N}\text{= 4}$ circular quiver Chern-Simons-matter theories
• Wilson-loop One-point Functions in ABJM Theory
• Exact results for Wilson loops in orbifold ABJM theory
• Loop Operators in Three-Dimensional $\mathcal{N}=2$ Fishnet Theories
• Surface Operators in Superspace
• More Fermionic Supersymmetric Wilson loops in Four Dimensions