  Fractional superstrings are recently-proposed generalizations of the
traditional superstrings and heterotic strings. They have critical spacetime
dimensions which are less than ten, and in this paper we investigate
model-building for the heterotic versions of these new theories. We concentrate
on the cases with critical spacetime dimensions four and six, and find that a
correspondence can be drawn between the new fractional superstring models and a
special subset of the traditional heterotic string models. This allows us to
generate the partition functions of the new models, and demonstrate that their
number is indeed relatively limited. It also appears that these strings have
uniquely natural compactifications to lower dimensions. In particular, the
fractional superstring with critical dimension six has a natural interpretation
in four-dimensional spacetime.
