MSSM matter fields will be suppressed by an additional loop factor, just like in ordinary gaugino mediation. An important difference between the 4D and 5D approach is that in the 4D approach Planck suppressed contact terms must be subleading, because (contrary to the 5D case) they have no further exponential suppression. The reason for this is that the notion of locality from gravity’s point of view is lost, if (as we will imagine) 4D gravity is minimally included into the theory. Thus from this point of view the spirit of these models more closely resembles that of gauge mediation, where the Planck suppressed operators should also be negligible. However, the resulting mass spectrum agrees with that of gaugino mediation, and differs from the generic gauge-mediated spectrum.

The paper is organized as follows: in Section 2 we give the construction of the supersymmetric lattice models and check that the perturbative mass spectrum agrees with that of the ${\cal N}=1$ 5D theory. In Section 3 we show how to include flavors into the construction, and present the orbifold models. Using these results we present the 4D models for gaugino mediation in Section 4, and conclude in Section 5.

The construction of supersymmetric 