  In order to produce a low energy effective field theory from a string model,
it is necessary to specify a vacuum state. In order that this vacuum be
supersymmetric, it is well known that all field expectation values must be
along so-called flat directions, leaving the F- and D-terms of the scalar
potential to be zero. The situation becomes particularly interesting when one
attempts to realize such directions while assigning VEVS to fields transforming
under non-Abelian representations of the gauge group. Since the expectation
value is now shared among multiple components of a field, satisfaction of
flatness becomes an inherently geometrical problem in the group space.
Furthermore, the possibility emerges that a single seemingly dangerous F-term
might experience a self-cancellation among its components. The hope exists that
the geometric language can provide an intuitive and immediate recognition of
when the D and F conditions are simultaneously compatible, as well as a
powerful tool for their comprehensive classification. This is the avenue
explored in this paper, and applied to the cases of SU(2) and SO(2N), relevant
respectively to previous attempts at reproducing the MSSM and the flipped SU(5)
GUT. Geometrical interpretation of non-Abelian flat directions finds
application to M-theory through the recent conjecture of equivalence between
D-term strings and wrapped D-branes of Type II theory. Knowledge of the
geometry of the flat direction "landscape" of a D-term string model could yield
information about the dual brane model. It is hoped that the techniques
encountered will be of benefit in extending the viability of the
quasi-realistic phenomenologies already developed.
