  We study the first order form of the NS string sigma model allowing for
worldsheet couplings corresponding on the target space to a bi-vector, a
two-form and an inverse metric. Lifting the topological sector of this action
to three dimensions produces several Wess-Zumino like terms which encode the
bi-vector generalization of the Courant bracket. This bracket may be familiar
to physicists through the (H_{ijk},F_{ij}^{k},Q_i^{jk},R^{ijk}) notation for
non-geometric backgrounds introduced by Shelton-Taylor-Wecht. The
non-geometricity of the string theory in encoded in the global properties of
the bi-vector, when the bi-vector is a section then the string theory is
geometric. Another interesting situation emerges when one considers membrane
actions which are not equivalent to string theories on the boundary of the
membrane. Such a situation arises when one attempts to describe the so-called
R-space (the third T-dual of a T^3 with H_3 flux). This model appears to be, at
least classically, described by a membrane sigma model, not a string theory.
Examples of geometric backgrounds with bi-vector couplings and non-vanishing
Q-coefficients are provided by gauged WZW models.
