Gapless edge modes in (4+1)-dimensional topologically massive tensor gauge theory and anomaly inflow for subsystem symmetry

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