Supersymmetric Wilson loops on S^3

Understand

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.