Abelian Chern-Simons theory on the lattice

I will discuss a formulation of an Abelian Chern-Simons theory on the lattice employing the modified Villain formalism. The theory suffers from a well-known problem of having extra zero modes in the Gaussian operator. I will argue that these zero modes are associated with a kind of subsystem symmetry which projects out almost all naive Wilson loops. The operators which survive are framed Wilson loops. These turn out to be topological charges of the associated one-form symmetry, and it has the correct topological spin and correlation functions.