  We have considered the most general gauge invariant five-dimensional action
of a second rank antisymmetric Kalb-Ramond tensor gauge theory, including a
topological term of the form $\epsilon^{ABLMN}B_{AB}H_{LMN}$ in a
Randall-Sundrum scenario. Such a tensor field $B_{AB}$ (whose rank-3 field
strength tensor is $H_{LMN}$), which appears in the massless sector of a
heterotic string theory, is assumed to coexist with the gravity in the bulk.
The third rank field strength corresponding to the Kalb-Ramond field has a
well-known geometric interpretation as the spacetime torsion. The only
non-trivial classical solutions corresponding to the effective four-dimensional
action are found to be self-dual or anti-selfdual Kalb-Ramond fields. This
ensures that the four-dimensional effective action on the brane is
parity-conserving. The massive modes for both cases, lying in the TeV range,
are related to the fundamental parameters of the theory. These modes can be
within the kinematic reach of forthcoming TeV scale experiments. However, the
couplings of the massless as well as massive Kalb-Ramond modes with matter on
the visible brane are found to be suppressed vis-a-vis that of the graviton by
the warp factor, whence the conclusion is that both the massless and the
massive torsion modes appear much weaker than curvature to an observer on the
visible brane.
