Charges in the UV completion of neutral electrodynamics

Abstract

A theory with a non-compact form-symmetry is described by two closed form fields of degrees k and d – k. Effective theory examples are non-linear electrodynamics, a photon field coupled to a neutron field, and a low energy Goldstone boson. We show these models cannot be completed in the UV without breaking the non-compact form-symmetry down to a compact one. This amounts to the existence of electric or magnetic charges. A theory with an unbroken non-compact k-form symmetry is massless and free.