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The half-supersymmetric Wilson loop in $\mathcal N=4$ SYM is arguably thecentral non-local operator in the AdS/CFT correspondence. On the field theoryside, the vacuum expectation values of Wilson loops in arbitraryrepresentations of $SU(N)$ are captured to all orders in perturbation theory bya Gaussian matrix model. Of prominent interest are the $k$-symmetric and$k$-antisymmetric representations, whose gravitational description is given interms of D3- and D5-branes, respectively, with fluxes in their world volumes.At leading order in $N$ and $\lambda$ the agreement in both cases is exact. Inthis note we explore the structure of the next-to-leading order correction inthe matrix model and compare with existing string theory calculations. We findagreement in the functional dependence on $k$ but a mismatch in the numericalcoefficients.

One-loop Structure of Higher Rank Wilson Loops in AdS/CFT