On the D3-brane description of some 1/4 BPS Wilson loops

Recently it has been proposed that Wilson loops in high-dimensional representations in ≤ 4 supersymmetric Yang-Mills theory (or multiply wrapped loops) are described by D-branes in AdS₅ × S⁵, rather than by fundamental strings. Thus far explicit D3-brane solutions have been only found in the case of the half-BPS circle or line. Here we present D3-brane solutions describing some 1/4 BPS loops. In one case, where the loop is conjectured to be given by a Gaussian matrix model, the action of the brane correctly reproduces the expectation value of the Wilson loop including all 1/N corrections at large λ. As in the corresponding string solution, here too we find two classical solutions, one stable and one not. The unstable one contributes exponentially small corrections that agree with the matrix model calculation.