Kähler potential is a more difficult task, since one needs to know the series expansion of the matrix of second derivatives of the inverse Kähler potential up to second order in the fields. This is in addition to knowing the Kähler potential up to second order. To calculate the second derivatives of the inverse Kähler potential to second order we would need to calculate the Kähler potential to fourth order, doubling the number of fields we have to consider simultaneously. This alone shows that this approach should be significantly more time consuming.

As a technical point we note that the Coleman-Weinberg contribution to $\Phi_0$’s mass derived in ISS is not valid away from the global ISS minimum. If we only include the one-loop masses derived in [@Intriligator:2006dd] and allow all fields to vary, then the numerical solution has negative eigenvalues in the Hessian. This apparent instability can be shown to be an artifact caused by the mismatch between the global minimum (the point at which ISS’s masses are correct) and the true minimum (in which they are not). While these effects are small we can re-calculate the one-loop contribution at the minimum of the tree-level plus one-loop potentials, we can 