valid below.

Locally supersymmetric ISS {#sec:Local ISS}
==========================

If one simply promotes ISS to having a local supersymmetry without including any additional physics, the results are not significantly perturbed near the minima of the SUSY theory.

However, the picture changes if any other terms appear in the superpotential. Any new physics that generates a non-zero $\<W\>$, necessary to have a finite gravitino mass and cancel the cosmological constant, will at least interact gravitationally with the moduli.

Even the simplest possible modification, the addition of a small ($\ll 1$) constant, $W_0$, to the superpotential, is sufficient to push the pseudo-moduli to large expectation values. This is not altogether surprising since the global, tree-level potential is independent of the pseudo-moduli and so their entire potential is given by Planck suppressed, non-renormalisable operators once supergravity corrections are included. As such, the natural scale for their expectation values is $M_p$.

However, one-loop effects should not be ignored. In the vicinity of the metastable point the logarithmic one-loop potential generates mass corrections of order $h^2\mu$ multiplied by a loop suppression factor. For comparison, the typical contribution to the logarithmic part of the one-loop potential from the gravitational effects is $(h^2\mu^3/M_{P})^{1/2}$ [^4]. Hence, the gravitational corrections 