On the D5-brane description of $\frac{1}{4}$-BPS Wilson loops in $\mathcal{N}=4$ super Yang-Mills theory

We construct the probe D5-brane solution in $Ad{S}_5\times S^5$ dual to the $\frac{1}{4}$-BPS latitude Wilson loop in $\mathcal{N}=4$ super Yang-Mills theory in the $k$-antisymmetric representation of $SU(N)$. The solution is exact in the latitude parameter ${\theta }_0$ and correctly reproduces the $\frac{1}{2}$-BPS limit. We compute the string charge $k$ and the renormalized on-shell action perturbatively to order $\mathcal{O}\left({\theta }_0^{10}\right)$ and find full agreement with the expectation value of the Wilson loop predicted by the Gaussian matrix model in the limit $N\sim k\to \mathrm{\infty }$, $\lambda \to \mathrm{\infty }$.