Lower-Form Symmetries

When gauging a $(d-1)$-form symmetry in $d$ spacetime dimensions, one formally expects the gauged theory to carry a dual $-1$-form symmetry. This work focuses on the study of such symmetries, in particular via the spacetime-filling topological operators that implement them, in two-dimensional field theory (with an eye towards general quantum field theory). As theories with $(d-1)$-form symmetries are known to be equivalent to direct sums of local theories, we review how gauging a $(d-1)$-form symmetry projects onto a single component in this sum, and explain how gauging the resulting $-1$-form symmetry restores the direct sum.