LAUSR

Subsystem symmetries are intermediate between global and gauge symmetries. One can treat these symmetries either like global symmetries that act on subregions of a system, or gauge symmetries that act on the regions transverse to the regions acted upon by the symmetry. We show that this latter interpretation can lead to an understanding of global, topology-dependent features in systems with subsystem symmetries. We demonstrate this with an exactly solvable lattice model constructed from a two-dimensional system of bosons coupled to a vector field with a one-dimensional subsystem symmetry. The model is shown to host a robust ground-state degeneracy that depends on the spatial topology of the underlying manifold, and localized zero-energy modes on corners of the system. A continuum field theory description of these phenomena is derived in terms of an anisotropic, modified version of the Abelian $K$-matrix Chern-Simons field theory. We show that this continuum description can lead to geometric-type effects such as corner states and edge states whose character depends on the orientation of the edge.