Supersymmetric Wilson loops on S3

This paper studies in great detail a family of supersymmetric Wilson loop operators in N = 4 supersymmetric Yang-Mills theory we have recently found. For a generic curve on an S-3 in space-time the loops preserve two supercharges but we will also study special cases which preserve 4, 8 and 16 supercharges. For certain loops we find the string theory dual explicitly and for the general case we show that string solutions satisfy a first order differential equation. This equation expresses the fact that the strings are pseudo-holomorphic with respect to a novel almost complex structure we construct on AdS(4) x S-2. We then discuss loops restricted to S-2 and provide evidence that they can be calculated in terms of similar observables in purely bosonic YM in two dimensions on the sphere.