  We consider (4+1)-dimensional topologically massive tensor gauge theory. This
theory is an analog of the (2+1)-dimensional topologically massive
Maxwell-Chern-Simons theory. If the space has a boundary, we find that a
(3+1)-dimensional gapless theory appears at the boundary. This gapless theory
is a chiral version of the (3+1)-dimensional $\varphi$ theory. This gapless
theory is protected by the anomaly inflow mechanism of subsystem symmetry. We
also consider the corner of our topologically massive tensor gauge theory, and
find that an infinite number of (1+1)-dimensional chiral bosons appear at the
corner.
