Wilson Loops in N=4 SYM and Fermion Droplets

The matrix models which are conjectured to compute the circle Wilson loop and its correlator with chiral primary operators are mapped onto normal matrix models. A fermion droplet picture analogous to the well-known one for chiral primary operators is shown to emerge in the large N limit. Several examples are computed. We find an interesting selection rule for the correlator of a single trace Wilson loop with a chiral primary operator. It can be non-zero only if the chiral primary is in a representation with a single hook. We show that the expectation value of the Wilson loop in a large representation labelled by a Young diagram with a single row has a first order phase transition between a regime where it is identical to a large column representation and a regime where it is a large wrapping number single trace Wilson loop.