On exact solvability of N=4 super Yang-Mills

We consider the ambitwistor description of N=4 supersymmetric extension of U(N) Yang-Mills theory on Minkowski space R3,1. It is shown that solutions of super-Yang-Mills equations are encoded in real analytic U(N)-valued functions on a domain in superambitwistor space LR5|6 of real dimension (5|6). This leads to a procedure for generating solutions of super-Yang-Mills equations on R3,1 via solving a Riemann-Hilbert-type factorization problem on two-spheres in LR5|6.