  A large class of four-dimensional supersymmetric ground states of closed
superstrings with a non-zero mass gap are constructed. For such ground states
we turn on chromo-magnetic fields as well as curvature. The exact spectrum as
function of the chromo-magnetic fields and curvature is derived. We examine the
behavior of the spectrum, and find that there is a maximal value for the
magnetic field $H_{\rm max}\sim M_{\rm planck}^2$. At this value all states
that couple to the magnetic field become infinitely massive and decouple. We
also find tachyonic instabilities for strong background fields of the order
${\cal O}(\mu M_{\rm planck})$ where $\mu$ is the mass gap of the theory.
Unlike the field theory case, we find that such ground states become stable
again for magnetic fields of the order ${\cal O}(M^2_{\rm planck})$. The
implications of these results are discussed.
