  In its traditional form, the string field in closed string field theory is
constrained by the level-matching condition, which is imposed beside the
action. By analogy with the similar problem for the Ramond sector, it was
understood by Okawa and Sakaguchi how to lift this condition and work with
unconstrained field by introducing spurious free fields. These authors also
pointed out that new backgrounds may exist thanks to a new gauge field which is
trivial on flat space, but can generate fluxes on a toroidal background. In
this paper, we perform a complete study of the free theory at the tachyonic and
massless levels with the aim of setting the stage for studying backgrounds
without level-matching.
