More Fermionic Supersymmetric Wilson loops in Four Dimensions

TL;DR

This paper constructs and analyzes new fermionic Wilson loops in four-dimensional supersymmetric gauge theories, demonstrating their properties and equivalence to known loops up to a certain perturbative order.

Contribution

It introduces generalized fermionic Wilson loops in 4D supersymmetric theories and verifies their cohomological equivalence to Zarembo loops at perturbative level.

Findings

Constructed supersymmetric fermionic Wilson loops in 4D theories.

Verified cohomological equivalence to Zarembo loops up to order g^4.

Computed expectation values in $ ext{N}=4$ super Yang-Mills.

Abstract

We construct supersymmetric fermionic Wilson loops along general curves in four-dimensional $\mathcal{N}=4$ super Yang-Mills theory and along general planar curves in $\mathcal{N}=2$ superconformal $SU(N)\times SU(N)$ quiver theory. These loops are generalizations of the Zarembo loops and are cohomologically equivalent to them. In $\mathcal{N}=4$ super Yang-Mills theory, we compute their expectation values and verify the cohomological equivalence relation up to the order $g^4$ in perturbation theory.