Gauging Modulated Symmetries: Bond Algebras, Higher-Form Symmetries, and Symmetry-Enriched Topological Order
The work develops a framework to characterize discrete Abelian modulated symmetries and their gauging in lattice systems. It uses modulation profiles as representations of space groups acting on internal symmetry groups, leading to periodic patterns. This allows for the systematic derivation of symmetry-allowed local interactions and gauging these symmetries results in Abelian crystalline symmetry-enriched topological phases (SETs).