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

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