  We present examples of four dimensional, non-supersymmetric field theories in
which ultraviolet supersymmetry breaking effects, such as bose-fermi splittings
and the vacuum energy, are suppressed by $(\alpha/4 \pi)^{N}$, where $\alpha$
is a weak coupling factor and $N$ can be made arbitrarily large. The particle
content and interactions of these models are conveniently represented by a
graph with sites and links, describing the gauge theory space structure. While
the theories are supersymmetric ``locally'' in theory space, supersymmetry can
be explicitly broken by topological obstructions.
