  We investigate the appearance of straight infinite Wilson lines lying on the
self-dual plane in the context of the Self Dual sector of the Yang Mills theory
and in a connection to the Lagrangian implementing the MHV vertices (MHV
Lagrangian) according to the Cachazo-Svrcek-Witten method. It was already
recognized in the past by two of the authors, that such Wilson line functional
provides the field transformation of positive helicity fields between the
Yang-Mills theory on the light-cone and the MHV Lagrangian. Here we discuss in
detail the connection to the Self Dual sector and we provide a new insight into
the solution for the minus helicity field transformation, which can be
expressed in terms of a functional derivative of the straight infinite Wilson
line on the self-dual plane.
