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

TL;DR

This paper constructs an exact D5-brane solution in AdS5×S5 that describes 1/4-BPS latitude Wilson loops in N=4 super Yang-Mills, matching matrix model predictions in the large N and k limit.

Contribution

It provides a new exact D5-brane solution for 1/4-BPS Wilson loops in N=4 SYM, extending previous 1/2-BPS results and confirming matrix model predictions.

Findings

Exact D5-brane solution for 1/4-BPS Wilson loops

Agreement with matrix model predictions at large N and k

Perturbative computation matches expected Wilson loop values

Abstract

We construct the probe D5-brane solution in $AdS_5\times S^5$ 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 $N\sim k\to\infty$, $\lambda\to\infty$.