  We study the supersymmetric extension of the Faddeev model in four
dimensions. The Faddeev model contains three dimensional soliton solutions and
we are interested in how these solitons are affected by supersymmetry. We
consider both the N=1 and N=2 extensions and find that in neither case it is
possible to supersymmetrize the model without adding additional bosonic terms.
There are essentially two ways of constructing the supersymmetric theory, one
that will lead to a model which allows for solitons and another that gives a
model where solitons are excluded.
  The N=2 model is studied since extending supersymmetry is the natural way of
including topological charges in the algebra. A lower bound to the mass is
obtained by computing the central charge. The result is that it is possible to
have a non-trivial lower bound on the mass, this in principle allows for
massive solitons.
