Compact Picture in Extended Superconformal Field Theories

There is a complex conformal transformation, which maps the $D$ - dimensional real Minkowski space on a bounded set in the $D$ - dimensional complex vector space. It generalizes the Cayley map from $D=1$ dimensions to higher space-time dimensions. This transformation provides a very convenient coordinate picture for Conformal Field Theories called compact picture. In this paper we extend the compact picture coordinates for superconformal field theories in four space-time dimensions.