Magnetic operators in 2D compact scalar field theories on the lattice

Abstract In lattice compact gauge theories, we must impose the admissibility condition to have well-defined topological sectors. The condition, however, usually forbids presence of magnetic operators, and it is not so trivial if one can study physics objects that depends on term, such as Witten effect, lattice. this paper, address question in case 2D scalars would be simplest examples having analogues monopole term. To define operator, propose “excision method,” which consists excising links (or bonds) an appropriate region containing operator defining dual a particular way. size excised O(1) units becomes point-like continuum limit. We give derivation ’t Hooft anomalies between electric symmetries also derive higher-group-like structure related effect.