Topological Order and Subsystem Symmetry

When a system is invariant under a subsystem symmetry, it is as if it has a "gauge" symmetry on particular subregions. Motivated by this obervation, we show that subsystem symmetries can lead to topological features remenescent of those found in topological gauge theories. This is done by considering a subsystem symmetry generalization of a Chern-Simons field theory. Because of the subsystem symmetry, this model has a robust ground state degeneracy on torus and localized zero energy corner modes.