One-loop structure of higher rank Wilson loops in AdS/CFT

The half-supersymmetric Wilson loop in N=4N=4 SYM is arguably the central non-local operator in the AdS/CFT correspondence. On the field theory side, the vacuum expectation values of Wilson loops in arbitrary representations of SU(N)SU(N) are captured to all orders in perturbation theory by a Gaussian matrix model. Of prominent interest are the k-symmetric and k-antisymmetric representations, whose gravitational description is given in terms of D3- and D5-branes, respectively, with fluxes in their world volumes. At leading order in N and λ the agreement in both cases is exact. In this note we explore the structure of the next-to-leading order correction in the matrix model and compare it with existing string theory calculations. We find agreement in the functional dependence on k but a mismatch in the numerical coefficients.