  We present 4D gauge theories which at low energies coincide with higher
dimensional supersymmetric (SUSY) gauge theories on a transverse lattice. We
show that in the simplest case of pure 5D SUSY Yang-Mills there is an
enhancement of SUSY in the continuum limit without fine-tuning. This result no
longer holds in the presence of matter fields, in which case fine-tuning is
necessary to ensure higher dimensional Lorentz invariance and supersymmetry. We
use this construction to generate 4D models which mimic gaugino mediation of
SUSY breaking. The way supersymmetry breaking is mediated in these models to
the MSSM is by assuming that the physical gauginos are a mixture of a number of
gauge eigenstate gauginos: one of these couples to the SUSY breaking sector,
while another couples to the MSSM matter fields. The lattice can be as coarse
as just two gauge groups while still obtaining the characteristic
gaugino-mediated soft breaking terms.
