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 AdS₅ × S⁵ dual to the $\frac{1}{4}$ \( \frac{1}{4} \) -BPS latitude Wilson loop in $\mathcal{N}$ \( \mathcal{N} \) = 4 super Yang-Mills theory in the k-antisymmetric representation of SU(N). The solution is exact in the latitude parameter θ₀ and correctly reproduces the $\frac{1}{2}$ \( \frac{1}{2} \) -BPS limit. We compute the string charge k and the renormalized on-shell action perturbatively to order $\mathcal{O}\left({\theta }_0^{10}\right)$ \( \mathcal{O}\left({\theta}_0^{10}\right) \) and find full agreement with the expectation value of the Wilson loop predicted by the Gaussian matrix model in the limit N ∼ k → ∞, λ → ∞.