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

TL;DR

This paper constructs new fermionic BPS Wilson loops in 4D $ ext{N}=2$ superconformal theories, revealing their supermatrix structure, supersymmetry properties, and potential for exploring gauge theory and duality structures.

Contribution

It introduces the first Drukker-Trancanelli type fermionic BPS Wilson loops in 4D $ ext{N}=2$ theories, with detailed analysis of their supersymmetry and geometric properties.

Findings

Constructed fermionic BPS Wilson loops with supermatrix connections.

Identified conditions for supersymmetry enhancement.

Demonstrated differences from previously known fermionic Wilson loops.

Abstract

We construct for the first time Drukker-Trancanelli (DT) type fermionic Bogomol\`nyi-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.