$\mathcal{N} = 4$ polygonal Wilson loops: fermions

TL;DR

This paper analyzes fermion contributions to null polygonal Wilson loops in $ ext{N}=4$ SYM, deriving strong coupling expansions and connecting results to string theory and instanton partition functions.

Contribution

It provides a systematic strong coupling expansion of fermion contributions to Wilson loops, including bound state formations, linking gauge theory, string theory, and instanton calculations.

Findings

Derived the leading order fermion-anti-fermion bound state contribution.

Reproduced the string minimal area result from fermionic expansions.

Applicable to Nekrasov instanton partition functions in $ ext{N}=2$ theories.

Abstract

The contributions of scalars and fermions to the null polygonal bosonic Wilson loops/gluon MHV scattering amplitudes in $\mathcal{N} = 4$ SYM are considered. We first examine the re-summation of scalars at strong coupling. Then, we disentangle the form of the fermion contribution and show its strong coupling expansion. In particular, we derive the leading order with the appearance of a fermion-anti-fermion bound state first and then effective multiple bound states thereof. This reproduces the string minimal area result and also applies to the Nekrasov instanton partition function $\mathcal{Z}$ of the $\mathcal{N}=2$ theories. Especially, in the latter case the method appears to be suitable for a systematic expansion.