On the Amplitude/Wilson Loop duality in $\mathcal{N}=2$ SCQCD

TL;DR

This paper calculates a specific two-loop four-point amplitude in $ ext{N}=2$ SCQCD and finds that the amplitude/Wilson loop duality, known in $ ext{N}=4$ SYM, does not hold in this theory at two loops.

Contribution

It extends previous two-loop amplitude calculations to $ ext{N}=2$ SCQCD and demonstrates the breakdown of the amplitude/Wilson loop duality in this context.

Findings

Amplitude/Wilson loop duality is broken at two loops in $ ext{N}=2$ SCQCD.

The difference with $ ext{N}=4$ SYM is a non-trivial function of kinematic variables.

The result confirms the duality's limitation beyond $ ext{N}=4$ SYM.

Abstract

We compute the four-point amplitude with external adjoint particles in $\mathcal{N}=2$ SCQCD at two loops using $\mathcal{N}=1$ superspace Feynman diagrams, extending the results of arXiv:1406.7283. We consider the diagrammatic difference with the corresponding process of $\mathcal{N}=4$ SYM finding a non vanishing result, which is a non trivial function of the kinematic variables. This demonstrates that in $\mathcal{N}=2$ SCQCD, even in the sector with external particles in the vector multiplet, the amplitude/Wilson loop duality is inevitably broken at two loops.