be included. While the quadratic one-loop potential is zero in the absence of gravity, the gravitational corrections generate a potential similar to the gravitational corrections to the tree-level, but controlled by an overall factor of $\frac{\Lambda^2}{32\pi^2}$ - as we show in appendix \[sec:appB\]. These potentials, combined with the tree-level, must be computed in order to obtain a reliable leading order estimate in general, with the quadratic potential being of particular interest if the number of fields is large and the cut-off close to the Planck scale.

In table \[table:Non-pert\] the row $\Lambda_{\mbox{non-pert.}}$ is the coefficient of the non-perturbative piece, introduced to compensate for the missing powers of $\Phi_{ij}$ that would be present in the determinant for a realistic number of flavours. Note, the F-term for $\Phi_0$ is not included since it is only shifted by corrections of order $\mu^3$, so $F_{\Phi_0}=h
 \mu^2+\mathcal{O}(\mu^3)$. For physically reasonable values of $\mu$ this effect is negligible. Also, $\Lambda=10^{-2}$, (i.e. the string/GUT scale) throughout tables \[table:Non-pert\] and \[table:Mu dep\]. The reason is, this value of $\Lambda$ is sufficiently small and ensures that the quadratically divergent loop correction to the potential only creates a small shift from the tree-level result, leaving us with the logarithmic piece 