Fermionic Bogomolnyi-Prasad-Sommerfield Wilson loops in four-dimensional $\mathcal{N}=2$ superconformal gauge theories

Abstract

We construct for the first time Drukker-Trancanelli (DT) type fermionic Bogomolnyi-Prasad-Sommerfield (BPS) Wilson loops in four-dimensional $\mathcal{N}=2$ superconformal $SU(N)\times SU(N)$ quiver theory and $\mathcal{N}=4$ super Yang-Mills theory. The connections of these fermionic BPS Wilson loops have a supermatrix structure. We construct timelike BPS Wilson lines in Minkowski spacetime and circular BPS Wilson loops in Euclidean space. These Wilson loops involve dimensionful parameters. For generic values of parameters, they preserve one real (complex) supercharge in Lorentzian (Euclidean) signature. Supersymmetry enhancement for Wilson loops happens when the parameters satisfy certain constraints. The nature of such loops is quite different from the Wilson loop operators involving fermions constructed previously in the literature on four-dimensional gauge theories. We hope that further investigations of such new Wilson loops will explore deep structures in both the gauge theories and gauge/gravity dualities.

arXiv comment26 pages, no figures; v2, 27 pages, no figures, typos fixed, references added, minor changes; v3 29 pages, no figures, minor revision, typos fixed, references added; v3, 29 pages, no figures,minor reversion

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