  Is perturbative stability intimately tied with the existence of spacetime
fermions in string theory in more than two dimensions? Type 0'B string theory
in ten-dimensional flat space is a rare example of a non-tachyonic,
non-supersymmetric string theory with a purely bosonic closed string spectrum.
However, all known type 0' constructions exhibit massless NSNS tadpoles
signaling the fact that we are not expanding around a true vacuum of the
theory. In this note, we are searching for perturbatively stable examples of
type 0' string theory without massless tadpoles in backgrounds with a spatially
varying dilaton. We present two examples with this property in non-critical
string theories that exhibit four- and six-dimensional Poincare invariance. We
discuss the D-branes that can be embedded in this context and the type of gauge
theories that can be constructed in this manner. We also comment on the
embedding of these non-critical models in critical string theories and their
holographic (Little String Theory) interpretation and propose a general
conjecture for the role of asymptotic supersymmetry in perturbative string
theory.
