  We study a recently discovered family of 1/8-BPS supersymmetric Wilson loops
in N=4 super Yang-Mills theory and their string theory duals. The operators are
defined for arbitrary contours on a two-sphere in space-time, and they were
conjectured to be captured perturbatively by 2d bosonic Yang-Mills theory. In
the AdS dual, they are described by pseudo-holomorphic string surfaces living
on a certain submanifold of AdS_5 x S^5. We show that the regularized area of
these string surfaces is invariant under area preserving diffeomorphisms of the
boundary loop, in agreement with the conjecture. Further, we find a connection
between the pseudo-holomorphicity equations and an auxiliary sigma-model on
S^3, which may help to construct new 1/8-BPS string solutions. We also show
that the conjectured relation to 2d Yang-Mills implies that a connected
correlator of two Wilson loops is computed by a Hermitian Gaussian two-matrix
model. On the AdS dual side, we argue that the connected correlator is
described by two disconnected disks interacting through the exchange of
supergravity modes, and we show that this agrees with the strong coupling
planar limit of the two-matrix model.
