  Unimodular Gravity is a theory displaying Weyl rescalings of the metric and
transverse (volume-preserving) diffeomorphisms as gauge symmetries, as opposed
to the full set of diffeomorphisms displayed by General Relativity. Recently,
we presented a systematic comparison of both theories, concluding that both of
them are equivalent in everything but the behaviour of the cosmological
constant under radiative corrections. A careful study of how Unimodular Gravity
can be embedded in the string theory framework has not been provided yet and
was not analyzed there in detail. In this article, we provide such an explicit
analysis, filling the gap in the literature. We restrict ourselves to the
unoriented bosonic string theory in critical dimension for the sake of
simplicity, although we argue that no differences are expected for other string
theories. Our conclusions are that both a Diff and a WTDiff invariance
principle are equally valid for describing the massless excitations of the
string spectrum.
