  In this paper we study the consequences of the introduction of a flat
boundary on a 4D covariant rank-2 gauge theory described by a linear
combination of linearized gravity and covariant fracton theory. We show that
this theory gives rise to a Maxwell-Chern-Simons-like theory of two rank-2
traceless symmetric tensor fields. This induced 3D theory can be physically
traced back to the traceless scalar charge theory of fractons, where the
Chern-Simons-like term plays the role of a matter contribution. By further
imposing time reversal invariance on the boundary, the Chern-Simons-like term
disappears. Importantly, on the boundary of our 4D gauge theory we find a
generalized U(1) Ka\c{c}-Moody algebra and the induced 3D theory is
characterized by the conservation of the dipole moment.
