  We study the boundary theory of the $\mathbb{Z}_N$ X-cube model using a
continuum perspective, from which the exchange statistics of a subset of bulk
excitations can be recovered. We discuss various gapped boundary conditions
that either preserve or break the translation/rotation symmetries on the
boundary, and further present the corresponding ground state degeneracies on
$T^2\times I$. The low-energy physics is highly sensitive to the boundary
conditions: even the extensive part of the ground state degeneracy can vary
when different sets of boundary conditions are chosen on the two boundaries. We
also examine the anomaly inflow of the boundary theory and find that the X-cube
model is not the unique (3+1)d theory that cancels the 't Hooft anomaly of the
boundary.
