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

Recently it has been proposed that Wilson loops in high-dimensionalrepresentations in N=4 supersymmetric Yang-Mills theory (or multiply wrappedloops) are described by D-branes in AdS_5 x S^5, rather than by fundamentalstrings. Thus far explicit D3-brane solutions have been only found in the caseof the half-BPS circle or line. Here we present D3-brane solutions describingsome 1/4 BPS loops. In one case, where the loop is conjectured to be given by aGaussian matrix model, the action of the brane correctly reproduces theexpectation value of the Wilson loop including all 1/N corrections at large\lambda. As in the corresponding string solution, here too we find twoclassical solutions, one stable and one not. The unstable one contributesexponentially small corrections that agree with the matrix model calculation.Comment: 26 pages, 1 figure; v2: minor change