$q\bar{q}$ Potential at Finite T and Weak Coupling in $\mathcal{N}=4$

We compute the potential between a $q\bar{q}$ singlet for $\mathcal{N}=4$ $SUSY$ with gauge group $SU(N)$ at finite temperature $T$, large distances $rT \gg 1$andweakcoupling$g$. As a first step, we only consider at the electric modes and we compute the Debye mass $m_D$ where we find that each of the $8N$ bosonic degrees of freedom contributes to $m_D^2$ with $\frac{1}{6}{g}^2{T}^2$ while each of the $8N$ fermionic degrees of freedom contributes with $\frac{1}{12}{g}^2{T}^2$ yielding to $m_D^2=2N{g}^2{T}^2$. Then, motivated by results obtained in the literature from both, a weak coupling approach for $QCD$ and a large coupling investigation of $\mathcal{N}=4$ $SUSY$ through $AdS\mathrm{/}CFT$, we attempt to include magnetic mode corrections.