Charges in the UV completion of neutral electrodynamics

TL;DR

This paper demonstrates that theories with non-compact form-symmetries, such as certain electrodynamics models, cannot be UV completed without introducing charges that break the symmetry, implying such theories are massless and free.

Contribution

It shows that UV completion of non-compact form-symmetry theories necessarily involves symmetry breaking to include charges, revealing fundamental constraints on these models.

Findings

Non-compact form-symmetries cannot be UV completed without charges.

Unbroken non-compact form-symmetry implies a massless, free theory.

Charges necessarily break the non-compact symmetry in UV completion.

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.