  In a consistent heterotic string theory, the Kalb-Ramond field, which is the
source of spacetime torsion, is augmented by Yang-Mills and gravitational
Chern-Simons terms. When compactified to 4-dimensions and in the field theory
limit, such additional terms give rise to interactions with interesting
astrophysical predictions like rotation of plane of polarization for
electromagnetic and gravitational waves. On the other hand, if one is also
interested in coupling 2 or 3-form (Abelian or non-Abelian) gauge fields to
torsion, one needs another class of interaction. In this paper, we shall study
this interaction and offer some astrophysical and cosmological predictions. We
also comment on the possibility of such terms in loop quantum gravity where, if
the Barbero-Immirzi parameter is promoted to a field, acts as a source for
torsion.
