Holography and Geometry

I am studying the holography of non-local operators in field theories and the associated geometric structures. In particular, the Wilson surface in the 6d (2,0) theory is dual to M2-branes in M-theory on AdS7xS4. We would like to understand this duality better, and find out what property of the M2 is dual to the supersymmetry conditions of the surface. The approach to the problem is to use the much better understood duality between Wilson loops in 4d N=4 and minimal surfaces in IIB string theory on AdS5xS5 as a guide, making use of results there and known relationships between the two CFTs and the two dual theories, particularly the lifting of a loop in 4d to a surface in 6d.