$\<\Phi_0\>\propto \Lambda^2$. This dependence is not present in global theory and we found that only a very mild dependence was introduced by including supergravity corrections to the logarithmic effective potential, as we demonstrate in section \[sec:Numerics\]. Regrettably, this does not provide a rigorous test of the two approaches, due to the Kähler corrections being more postulated than derived in [@Haba:2008vj].

It is then not entirely surprising that our results differ markedly from those of [@Haba:2008vj]. This manifests itself primarily in our predictions for the expectation value of $\Phi_0$ which we find to be significantly smaller than $\mu$, irrespective of the value of the cut-off. This means that our model does not appear to be a good candidate for gauge mediation, since $\<\Phi_0\>^2<F_{\phi_0}$. However, the gravitational corrections to the quarks F-terms open the possibility that they could couple to a mediation sector and generate soft terms. We will return to this in section \[sec:SoftMasses\].

Analytic properties of STr$\mathcal{M}^2$
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For a canonical Kähler potential, the quadratic one-loop potential is given by $$\begin{aligned}
V_{\mbox{quad.}}=\frac{\mbox{STr}\mathcal{M}^2\Lambda^2}{32\pi^2} =   \frac{\Lambda^2 e^K}{16\pi^2} (N_f^2+2 N_f N_c-1)\left(\sum_i \left(W_i+X_iW \right)^2 \right) -  \frac{\Lambda^2 e^K}{8\pi^2} (N_f^2+2 N_f N_c) W^2.\end{aligned}$$ Where fields are taken to be real and $X_i$ runs over all 