there is a wide range of parameter space which leads to these values of $\tan\beta$. (In fact, even values of $\tan\beta$ very close to $1$ can naturally be obtained if $\mu$ is somewhat larger than $\tilde{m}$.) Below, we will use values of $\tilde{m}$ in Eq. (\[eq:m-tilde\]) as our guide in discussing ISS theories.

In this paper, we mostly assume that supersymmetry breaking is mediated to the GUT sector (the sector charged under the SM gauge group) at a high scale $M_*$ close to the UV cutoff scale $\Lambda$ of the unified theory, which we expect to be within an order of magnitude of the reduced Planck scale $M_{\rm Pl} \simeq 2.4 \times 10^{18}~{\rm GeV}$: $M_* 
\sim \Lambda \sim M_{\rm Pl}$. We then find that the gravitino mass $m_{3/2} = F/\sqrt{3} M_{\rm Pl}$ is roughly the same order of magnitude as $\tilde{m} \sim F/M_*$, where $F$ is the $F$-term VEV of the supersymmetry breaking field. In this paper we do not discriminate the sizes of the two, and treat them to be of the same order: $m_{3/2} 
\sim \tilde{m}$.

ISS with Intermediate Scale Colored Higgses {#sec:model}
===========================================

In this section, we present a simple model of ISS. It is representative of 